Given the Number 497,664,000, Calculate (Find) All the Factors (All the Divisors) of the Number 497,664,000 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 497,664,000

1. Carry out the prime factorization of the number 497,664,000:

The prime factorization of a number: finding the prime numbers that multiply together to make that number.

497,664,000 = 214 × 35 × 53
497,664,000 is not a prime number but a composite one.

» Online calculator. Check whether a number is prime or not. The prime factorization of composite numbers

* Prime number: a natural number that is divisible (divided evenly) only by 1 and itself. A prime number has exactly two factors: 1 and the number itself.
* Composite number: a natural number that has at least one other factor than 1 and itself.


2. Multiply the prime factors of the number 497,664,000

Multiply the prime factors involved in the prime factorization of the number in all their unique combinations, that give different results.

Also consider the exponents of these prime factors.

Also add 1 to the list of factors (divisors). All the numbers are divisible by 1.


All the factors (divisors) are listed below - in ascending order

The list of factors (divisors):

neither prime nor composite = 1
prime factor = 2
prime factor = 3
22 = 4
prime factor = 5
2 × 3 = 6
23 = 8
32 = 9
2 × 5 = 10
22 × 3 = 12
3 × 5 = 15
24 = 16
2 × 32 = 18
22 × 5 = 20
23 × 3 = 24
52 = 25
33 = 27
2 × 3 × 5 = 30
25 = 32
22 × 32 = 36
23 × 5 = 40
32 × 5 = 45
24 × 3 = 48
2 × 52 = 50
2 × 33 = 54
22 × 3 × 5 = 60
26 = 64
23 × 32 = 72
3 × 52 = 75
24 × 5 = 80
34 = 81
2 × 32 × 5 = 90
25 × 3 = 96
22 × 52 = 100
22 × 33 = 108
23 × 3 × 5 = 120
53 = 125
27 = 128
33 × 5 = 135
24 × 32 = 144
2 × 3 × 52 = 150
25 × 5 = 160
2 × 34 = 162
22 × 32 × 5 = 180
26 × 3 = 192
23 × 52 = 200
23 × 33 = 216
32 × 52 = 225
24 × 3 × 5 = 240
35 = 243
2 × 53 = 250
28 = 256
2 × 33 × 5 = 270
25 × 32 = 288
22 × 3 × 52 = 300
26 × 5 = 320
22 × 34 = 324
23 × 32 × 5 = 360
3 × 53 = 375
27 × 3 = 384
24 × 52 = 400
34 × 5 = 405
24 × 33 = 432
2 × 32 × 52 = 450
25 × 3 × 5 = 480
2 × 35 = 486
22 × 53 = 500
29 = 512
22 × 33 × 5 = 540
26 × 32 = 576
23 × 3 × 52 = 600
27 × 5 = 640
23 × 34 = 648
33 × 52 = 675
24 × 32 × 5 = 720
2 × 3 × 53 = 750
28 × 3 = 768
25 × 52 = 800
2 × 34 × 5 = 810
25 × 33 = 864
22 × 32 × 52 = 900
26 × 3 × 5 = 960
22 × 35 = 972
23 × 53 = 1,000
210 = 1,024
23 × 33 × 5 = 1,080
32 × 53 = 1,125
27 × 32 = 1,152
24 × 3 × 52 = 1,200
35 × 5 = 1,215
28 × 5 = 1,280
24 × 34 = 1,296
2 × 33 × 52 = 1,350
25 × 32 × 5 = 1,440
22 × 3 × 53 = 1,500
29 × 3 = 1,536
26 × 52 = 1,600
22 × 34 × 5 = 1,620
26 × 33 = 1,728
23 × 32 × 52 = 1,800
27 × 3 × 5 = 1,920
23 × 35 = 1,944
24 × 53 = 2,000
34 × 52 = 2,025
211 = 2,048
24 × 33 × 5 = 2,160
2 × 32 × 53 = 2,250
28 × 32 = 2,304
25 × 3 × 52 = 2,400
2 × 35 × 5 = 2,430
29 × 5 = 2,560
25 × 34 = 2,592
22 × 33 × 52 = 2,700
26 × 32 × 5 = 2,880
23 × 3 × 53 = 3,000
210 × 3 = 3,072
27 × 52 = 3,200
23 × 34 × 5 = 3,240
33 × 53 = 3,375
27 × 33 = 3,456
24 × 32 × 52 = 3,600
28 × 3 × 5 = 3,840
24 × 35 = 3,888
25 × 53 = 4,000
2 × 34 × 52 = 4,050
212 = 4,096
25 × 33 × 5 = 4,320
22 × 32 × 53 = 4,500
29 × 32 = 4,608
26 × 3 × 52 = 4,800
22 × 35 × 5 = 4,860
210 × 5 = 5,120
26 × 34 = 5,184
23 × 33 × 52 = 5,400
27 × 32 × 5 = 5,760
24 × 3 × 53 = 6,000
35 × 52 = 6,075
211 × 3 = 6,144
28 × 52 = 6,400
24 × 34 × 5 = 6,480
2 × 33 × 53 = 6,750
28 × 33 = 6,912
25 × 32 × 52 = 7,200
29 × 3 × 5 = 7,680
25 × 35 = 7,776
26 × 53 = 8,000
22 × 34 × 52 = 8,100
213 = 8,192
26 × 33 × 5 = 8,640
23 × 32 × 53 = 9,000
210 × 32 = 9,216
27 × 3 × 52 = 9,600
23 × 35 × 5 = 9,720
34 × 53 = 10,125
211 × 5 = 10,240
27 × 34 = 10,368
24 × 33 × 52 = 10,800
28 × 32 × 5 = 11,520
25 × 3 × 53 = 12,000
2 × 35 × 52 = 12,150
212 × 3 = 12,288
29 × 52 = 12,800
25 × 34 × 5 = 12,960
22 × 33 × 53 = 13,500
29 × 33 = 13,824
26 × 32 × 52 = 14,400
210 × 3 × 5 = 15,360
26 × 35 = 15,552
27 × 53 = 16,000
23 × 34 × 52 = 16,200
214 = 16,384
27 × 33 × 5 = 17,280
24 × 32 × 53 = 18,000
211 × 32 = 18,432
28 × 3 × 52 = 19,200
24 × 35 × 5 = 19,440
2 × 34 × 53 = 20,250
212 × 5 = 20,480
28 × 34 = 20,736
25 × 33 × 52 = 21,600
This list continues below...

... This list continues from above
29 × 32 × 5 = 23,040
26 × 3 × 53 = 24,000
22 × 35 × 52 = 24,300
213 × 3 = 24,576
210 × 52 = 25,600
26 × 34 × 5 = 25,920
23 × 33 × 53 = 27,000
210 × 33 = 27,648
27 × 32 × 52 = 28,800
35 × 53 = 30,375
211 × 3 × 5 = 30,720
27 × 35 = 31,104
28 × 53 = 32,000
24 × 34 × 52 = 32,400
28 × 33 × 5 = 34,560
25 × 32 × 53 = 36,000
212 × 32 = 36,864
29 × 3 × 52 = 38,400
25 × 35 × 5 = 38,880
22 × 34 × 53 = 40,500
213 × 5 = 40,960
29 × 34 = 41,472
26 × 33 × 52 = 43,200
210 × 32 × 5 = 46,080
27 × 3 × 53 = 48,000
23 × 35 × 52 = 48,600
214 × 3 = 49,152
211 × 52 = 51,200
27 × 34 × 5 = 51,840
24 × 33 × 53 = 54,000
211 × 33 = 55,296
28 × 32 × 52 = 57,600
2 × 35 × 53 = 60,750
212 × 3 × 5 = 61,440
28 × 35 = 62,208
29 × 53 = 64,000
25 × 34 × 52 = 64,800
29 × 33 × 5 = 69,120
26 × 32 × 53 = 72,000
213 × 32 = 73,728
210 × 3 × 52 = 76,800
26 × 35 × 5 = 77,760
23 × 34 × 53 = 81,000
214 × 5 = 81,920
210 × 34 = 82,944
27 × 33 × 52 = 86,400
211 × 32 × 5 = 92,160
28 × 3 × 53 = 96,000
24 × 35 × 52 = 97,200
212 × 52 = 102,400
28 × 34 × 5 = 103,680
25 × 33 × 53 = 108,000
212 × 33 = 110,592
29 × 32 × 52 = 115,200
22 × 35 × 53 = 121,500
213 × 3 × 5 = 122,880
29 × 35 = 124,416
210 × 53 = 128,000
26 × 34 × 52 = 129,600
210 × 33 × 5 = 138,240
27 × 32 × 53 = 144,000
214 × 32 = 147,456
211 × 3 × 52 = 153,600
27 × 35 × 5 = 155,520
24 × 34 × 53 = 162,000
211 × 34 = 165,888
28 × 33 × 52 = 172,800
212 × 32 × 5 = 184,320
29 × 3 × 53 = 192,000
25 × 35 × 52 = 194,400
213 × 52 = 204,800
29 × 34 × 5 = 207,360
26 × 33 × 53 = 216,000
213 × 33 = 221,184
210 × 32 × 52 = 230,400
23 × 35 × 53 = 243,000
214 × 3 × 5 = 245,760
210 × 35 = 248,832
211 × 53 = 256,000
27 × 34 × 52 = 259,200
211 × 33 × 5 = 276,480
28 × 32 × 53 = 288,000
212 × 3 × 52 = 307,200
28 × 35 × 5 = 311,040
25 × 34 × 53 = 324,000
212 × 34 = 331,776
29 × 33 × 52 = 345,600
213 × 32 × 5 = 368,640
210 × 3 × 53 = 384,000
26 × 35 × 52 = 388,800
214 × 52 = 409,600
210 × 34 × 5 = 414,720
27 × 33 × 53 = 432,000
214 × 33 = 442,368
211 × 32 × 52 = 460,800
24 × 35 × 53 = 486,000
211 × 35 = 497,664
212 × 53 = 512,000
28 × 34 × 52 = 518,400
212 × 33 × 5 = 552,960
29 × 32 × 53 = 576,000
213 × 3 × 52 = 614,400
29 × 35 × 5 = 622,080
26 × 34 × 53 = 648,000
213 × 34 = 663,552
210 × 33 × 52 = 691,200
214 × 32 × 5 = 737,280
211 × 3 × 53 = 768,000
27 × 35 × 52 = 777,600
211 × 34 × 5 = 829,440
28 × 33 × 53 = 864,000
212 × 32 × 52 = 921,600
25 × 35 × 53 = 972,000
212 × 35 = 995,328
213 × 53 = 1,024,000
29 × 34 × 52 = 1,036,800
213 × 33 × 5 = 1,105,920
210 × 32 × 53 = 1,152,000
214 × 3 × 52 = 1,228,800
210 × 35 × 5 = 1,244,160
27 × 34 × 53 = 1,296,000
214 × 34 = 1,327,104
211 × 33 × 52 = 1,382,400
212 × 3 × 53 = 1,536,000
28 × 35 × 52 = 1,555,200
212 × 34 × 5 = 1,658,880
29 × 33 × 53 = 1,728,000
213 × 32 × 52 = 1,843,200
26 × 35 × 53 = 1,944,000
213 × 35 = 1,990,656
214 × 53 = 2,048,000
210 × 34 × 52 = 2,073,600
214 × 33 × 5 = 2,211,840
211 × 32 × 53 = 2,304,000
211 × 35 × 5 = 2,488,320
28 × 34 × 53 = 2,592,000
212 × 33 × 52 = 2,764,800
213 × 3 × 53 = 3,072,000
29 × 35 × 52 = 3,110,400
213 × 34 × 5 = 3,317,760
210 × 33 × 53 = 3,456,000
214 × 32 × 52 = 3,686,400
27 × 35 × 53 = 3,888,000
214 × 35 = 3,981,312
211 × 34 × 52 = 4,147,200
212 × 32 × 53 = 4,608,000
212 × 35 × 5 = 4,976,640
29 × 34 × 53 = 5,184,000
213 × 33 × 52 = 5,529,600
214 × 3 × 53 = 6,144,000
210 × 35 × 52 = 6,220,800
214 × 34 × 5 = 6,635,520
211 × 33 × 53 = 6,912,000
28 × 35 × 53 = 7,776,000
212 × 34 × 52 = 8,294,400
213 × 32 × 53 = 9,216,000
213 × 35 × 5 = 9,953,280
210 × 34 × 53 = 10,368,000
214 × 33 × 52 = 11,059,200
211 × 35 × 52 = 12,441,600
212 × 33 × 53 = 13,824,000
29 × 35 × 53 = 15,552,000
213 × 34 × 52 = 16,588,800
214 × 32 × 53 = 18,432,000
214 × 35 × 5 = 19,906,560
211 × 34 × 53 = 20,736,000
212 × 35 × 52 = 24,883,200
213 × 33 × 53 = 27,648,000
210 × 35 × 53 = 31,104,000
214 × 34 × 52 = 33,177,600
212 × 34 × 53 = 41,472,000
213 × 35 × 52 = 49,766,400
214 × 33 × 53 = 55,296,000
211 × 35 × 53 = 62,208,000
213 × 34 × 53 = 82,944,000
214 × 35 × 52 = 99,532,800
212 × 35 × 53 = 124,416,000
214 × 34 × 53 = 165,888,000
213 × 35 × 53 = 248,832,000
214 × 35 × 53 = 497,664,000

The final answer:
(scroll down)

497,664,000 has 360 factors (divisors):
1; 2; 3; 4; 5; 6; 8; 9; 10; 12; 15; 16; 18; 20; 24; 25; 27; 30; 32; 36; 40; 45; 48; 50; 54; 60; 64; 72; 75; 80; 81; 90; 96; 100; 108; 120; 125; 128; 135; 144; 150; 160; 162; 180; 192; 200; 216; 225; 240; 243; 250; 256; 270; 288; 300; 320; 324; 360; 375; 384; 400; 405; 432; 450; 480; 486; 500; 512; 540; 576; 600; 640; 648; 675; 720; 750; 768; 800; 810; 864; 900; 960; 972; 1,000; 1,024; 1,080; 1,125; 1,152; 1,200; 1,215; 1,280; 1,296; 1,350; 1,440; 1,500; 1,536; 1,600; 1,620; 1,728; 1,800; 1,920; 1,944; 2,000; 2,025; 2,048; 2,160; 2,250; 2,304; 2,400; 2,430; 2,560; 2,592; 2,700; 2,880; 3,000; 3,072; 3,200; 3,240; 3,375; 3,456; 3,600; 3,840; 3,888; 4,000; 4,050; 4,096; 4,320; 4,500; 4,608; 4,800; 4,860; 5,120; 5,184; 5,400; 5,760; 6,000; 6,075; 6,144; 6,400; 6,480; 6,750; 6,912; 7,200; 7,680; 7,776; 8,000; 8,100; 8,192; 8,640; 9,000; 9,216; 9,600; 9,720; 10,125; 10,240; 10,368; 10,800; 11,520; 12,000; 12,150; 12,288; 12,800; 12,960; 13,500; 13,824; 14,400; 15,360; 15,552; 16,000; 16,200; 16,384; 17,280; 18,000; 18,432; 19,200; 19,440; 20,250; 20,480; 20,736; 21,600; 23,040; 24,000; 24,300; 24,576; 25,600; 25,920; 27,000; 27,648; 28,800; 30,375; 30,720; 31,104; 32,000; 32,400; 34,560; 36,000; 36,864; 38,400; 38,880; 40,500; 40,960; 41,472; 43,200; 46,080; 48,000; 48,600; 49,152; 51,200; 51,840; 54,000; 55,296; 57,600; 60,750; 61,440; 62,208; 64,000; 64,800; 69,120; 72,000; 73,728; 76,800; 77,760; 81,000; 81,920; 82,944; 86,400; 92,160; 96,000; 97,200; 102,400; 103,680; 108,000; 110,592; 115,200; 121,500; 122,880; 124,416; 128,000; 129,600; 138,240; 144,000; 147,456; 153,600; 155,520; 162,000; 165,888; 172,800; 184,320; 192,000; 194,400; 204,800; 207,360; 216,000; 221,184; 230,400; 243,000; 245,760; 248,832; 256,000; 259,200; 276,480; 288,000; 307,200; 311,040; 324,000; 331,776; 345,600; 368,640; 384,000; 388,800; 409,600; 414,720; 432,000; 442,368; 460,800; 486,000; 497,664; 512,000; 518,400; 552,960; 576,000; 614,400; 622,080; 648,000; 663,552; 691,200; 737,280; 768,000; 777,600; 829,440; 864,000; 921,600; 972,000; 995,328; 1,024,000; 1,036,800; 1,105,920; 1,152,000; 1,228,800; 1,244,160; 1,296,000; 1,327,104; 1,382,400; 1,536,000; 1,555,200; 1,658,880; 1,728,000; 1,843,200; 1,944,000; 1,990,656; 2,048,000; 2,073,600; 2,211,840; 2,304,000; 2,488,320; 2,592,000; 2,764,800; 3,072,000; 3,110,400; 3,317,760; 3,456,000; 3,686,400; 3,888,000; 3,981,312; 4,147,200; 4,608,000; 4,976,640; 5,184,000; 5,529,600; 6,144,000; 6,220,800; 6,635,520; 6,912,000; 7,776,000; 8,294,400; 9,216,000; 9,953,280; 10,368,000; 11,059,200; 12,441,600; 13,824,000; 15,552,000; 16,588,800; 18,432,000; 19,906,560; 20,736,000; 24,883,200; 27,648,000; 31,104,000; 33,177,600; 41,472,000; 49,766,400; 55,296,000; 62,208,000; 82,944,000; 99,532,800; 124,416,000; 165,888,000; 248,832,000 and 497,664,000
out of which 3 prime factors: 2; 3 and 5
497,664,000 and 1 are sometimes called improper factors, the others are called proper factors (proper divisors).

A quick way to find the factors (the divisors) of a number is to break it down into prime factors.

Then multiply the prime factors and their exponents, if any, in all their different combinations.


Other similar operations of calculating factors (divisors):

» What are all the proper, improper and prime factors (divisors) of the number 497,663,994?

» What are all the proper, improper and prime factors (divisors) of the number 497,664,006?


Calculate all the divisors (factors) of the given numbers

How to calculate (find) all the factors (divisors) of a number:

Break down the number into prime factors. Then multiply its prime factors in all their unique combinations, that give different results.

To calculate the common factors of two numbers:

The common factors (divisors) of two numbers are all the factors of the greatest common factor, gcf.

Calculate the greatest (highest) common factor (divisor) of the two numbers, gcf (hcf, gcd).

Break down the GCF into prime factors. Then multiply its prime factors in all their unique combinations, that give different results.

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The list of all the calculated factors (divisors) of one or two numbers

Factors (divisors), common factors (common divisors), the greatest common factor, GCF (also called the greatest common divisor, GCD, or the highest common factor, HCF)

  • If the number "t" is a factor (divisor) of the number "a" then in the prime factorization of "t" we will only encounter prime factors that also occur in the prime factorization of "a".
  • If there are exponents involved, the maximum value of an exponent for any base of a power that is found in the prime factorization of "t" (powers, or multiplicities) is at most equal to the exponent of the same base that is involved in the prime factorization of "a".
  • Hint: 23 = 2 × 2 × 2 = 8. 2 is called the base and 3 is the exponent. 23 is the power and 8 is the value of the power. We sometimes say that the number 2 is raised to the power of 3.
  • For example, 12 is a factor (divisor) of 120 - the remainder is zero when dividing 120 by 12.
  • Let's look at the prime factorization of both numbers and notice the bases and the exponents that occur in the prime factorization of both numbers:
  • 12 = 2 × 2 × 3 = 22 × 3
  • 120 = 2 × 2 × 2 × 3 × 5 = 23 × 3 × 5
  • 120 contains all the prime factors of 12, and all its bases' exponents are higher than those of 12.
  • If "t" is a common factor (divisor) of "a" and "b", then the prime factorization of "t" contains only the common prime factors involved in the prime factorizations of both "a" and "b".
  • If there are exponents involved, the maximum value of an exponent for any base of a power that is found in the prime factorization of "t" is at most equal to the minimum of the exponents of the same base that is involved in the prime factorization of both "a" and "b".
  • For example, 12 is the common factor of 48 and 360.
  • The remainder is zero when dividing either 48 or 360 by 12.
  • Here there are the prime factorizations of the three numbers, 12, 48 and 360:
  • 12 = 22 × 3
  • 48 = 24 × 3
  • 360 = 23 × 32 × 5
  • Please note that 48 and 360 have more factors (divisors): 2, 3, 4, 6, 8, 12, 24. Among them, 24 is the greatest common factor, GCF (or the greatest common divisor, GCD, or the highest common factor, HCF) of 48 and 360.
  • The greatest common factor, GCF, of two numbers, "a" and "b", is the product of all the common prime factors involved in the prime factorizations of both "a" and "b", taken by the lowest exponents.
  • Based on this rule it is calculated the greatest common factor, GCF, (or the greatest common divisor GCD, HCF) of several numbers, as shown in the example below...
  • GCF, GCD (1,260; 3,024; 5,544) = ?
  • 1,260 = 22 × 32
  • 3,024 = 24 × 32 × 7
  • 5,544 = 23 × 32 × 7 × 11
  • The common prime factors are:
  • 2 - its lowest exponent (multiplicity) is: min.(2; 3; 4) = 2
  • 3 - its lowest exponent (multiplicity) is: min.(2; 2; 2) = 2
  • GCF, GCD (1,260; 3,024; 5,544) = 22 × 32 = 252
  • Coprime numbers:
  • If two numbers "a" and "b" have no other common factors (divisors) than 1, gfc, gcd, hcf (a; b) = 1, then the numbers "a" and "b" are called coprime (or relatively prime).
  • Factors of the GCF
  • If "a" and "b" are not coprime, then every common factor (divisor) of "a" and "b" is a also a factor (divisor) of the greatest common factor, GCF (greatest common divisor, GCD, highest common factor, HCF) of "a" and "b".