Calculate and Count All the Factors of 501,760,000. Online Calculator

All the factors (divisors) of the number 501,760,000. How important is the prime factorization of the number

1. Carry out the prime factorization of the number 501,760,000:

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

501,760,000 = 214 × 54 × 72
501,760,000 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 (decomposition into prime factors)

* 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.


How to count the number of factors of a number?

If a number N is prime factorized as:
N = am × bk × cz
where a, b, c are the prime factors and m, k, z are their exponents, natural numbers, ....

Then the number of factors of the number N can be calculated as:
n = (m + 1) × (k + 1) × (z + 1)

In our case, the number of factors is calculated as:

n = (14 + 1) × (4 + 1) × (2 + 1) = 15 × 5 × 3 = 225

But to actually calculate the factors, see below...

2. Multiply the prime factors of the number 501,760,000

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
22 = 4
prime factor = 5
prime factor = 7
23 = 8
2 × 5 = 10
2 × 7 = 14
24 = 16
22 × 5 = 20
52 = 25
22 × 7 = 28
25 = 32
5 × 7 = 35
23 × 5 = 40
72 = 49
2 × 52 = 50
23 × 7 = 56
26 = 64
2 × 5 × 7 = 70
24 × 5 = 80
2 × 72 = 98
22 × 52 = 100
24 × 7 = 112
53 = 125
27 = 128
22 × 5 × 7 = 140
25 × 5 = 160
52 × 7 = 175
22 × 72 = 196
23 × 52 = 200
25 × 7 = 224
5 × 72 = 245
2 × 53 = 250
28 = 256
23 × 5 × 7 = 280
26 × 5 = 320
2 × 52 × 7 = 350
23 × 72 = 392
24 × 52 = 400
26 × 7 = 448
2 × 5 × 72 = 490
22 × 53 = 500
29 = 512
24 × 5 × 7 = 560
54 = 625
27 × 5 = 640
22 × 52 × 7 = 700
24 × 72 = 784
25 × 52 = 800
53 × 7 = 875
27 × 7 = 896
22 × 5 × 72 = 980
23 × 53 = 1,000
210 = 1,024
25 × 5 × 7 = 1,120
52 × 72 = 1,225
2 × 54 = 1,250
28 × 5 = 1,280
23 × 52 × 7 = 1,400
25 × 72 = 1,568
26 × 52 = 1,600
2 × 53 × 7 = 1,750
28 × 7 = 1,792
23 × 5 × 72 = 1,960
24 × 53 = 2,000
211 = 2,048
26 × 5 × 7 = 2,240
2 × 52 × 72 = 2,450
22 × 54 = 2,500
29 × 5 = 2,560
24 × 52 × 7 = 2,800
26 × 72 = 3,136
27 × 52 = 3,200
22 × 53 × 7 = 3,500
29 × 7 = 3,584
24 × 5 × 72 = 3,920
25 × 53 = 4,000
212 = 4,096
54 × 7 = 4,375
27 × 5 × 7 = 4,480
22 × 52 × 72 = 4,900
23 × 54 = 5,000
210 × 5 = 5,120
25 × 52 × 7 = 5,600
53 × 72 = 6,125
27 × 72 = 6,272
28 × 52 = 6,400
23 × 53 × 7 = 7,000
210 × 7 = 7,168
25 × 5 × 72 = 7,840
26 × 53 = 8,000
213 = 8,192
2 × 54 × 7 = 8,750
28 × 5 × 7 = 8,960
23 × 52 × 72 = 9,800
24 × 54 = 10,000
211 × 5 = 10,240
26 × 52 × 7 = 11,200
2 × 53 × 72 = 12,250
28 × 72 = 12,544
29 × 52 = 12,800
24 × 53 × 7 = 14,000
211 × 7 = 14,336
26 × 5 × 72 = 15,680
27 × 53 = 16,000
214 = 16,384
22 × 54 × 7 = 17,500
29 × 5 × 7 = 17,920
24 × 52 × 72 = 19,600
25 × 54 = 20,000
212 × 5 = 20,480
This list continues below...

... This list continues from above
27 × 52 × 7 = 22,400
22 × 53 × 72 = 24,500
29 × 72 = 25,088
210 × 52 = 25,600
25 × 53 × 7 = 28,000
212 × 7 = 28,672
54 × 72 = 30,625
27 × 5 × 72 = 31,360
28 × 53 = 32,000
23 × 54 × 7 = 35,000
210 × 5 × 7 = 35,840
25 × 52 × 72 = 39,200
26 × 54 = 40,000
213 × 5 = 40,960
28 × 52 × 7 = 44,800
23 × 53 × 72 = 49,000
210 × 72 = 50,176
211 × 52 = 51,200
26 × 53 × 7 = 56,000
213 × 7 = 57,344
2 × 54 × 72 = 61,250
28 × 5 × 72 = 62,720
29 × 53 = 64,000
24 × 54 × 7 = 70,000
211 × 5 × 7 = 71,680
26 × 52 × 72 = 78,400
27 × 54 = 80,000
214 × 5 = 81,920
29 × 52 × 7 = 89,600
24 × 53 × 72 = 98,000
211 × 72 = 100,352
212 × 52 = 102,400
27 × 53 × 7 = 112,000
214 × 7 = 114,688
22 × 54 × 72 = 122,500
29 × 5 × 72 = 125,440
210 × 53 = 128,000
25 × 54 × 7 = 140,000
212 × 5 × 7 = 143,360
27 × 52 × 72 = 156,800
28 × 54 = 160,000
210 × 52 × 7 = 179,200
25 × 53 × 72 = 196,000
212 × 72 = 200,704
213 × 52 = 204,800
28 × 53 × 7 = 224,000
23 × 54 × 72 = 245,000
210 × 5 × 72 = 250,880
211 × 53 = 256,000
26 × 54 × 7 = 280,000
213 × 5 × 7 = 286,720
28 × 52 × 72 = 313,600
29 × 54 = 320,000
211 × 52 × 7 = 358,400
26 × 53 × 72 = 392,000
213 × 72 = 401,408
214 × 52 = 409,600
29 × 53 × 7 = 448,000
24 × 54 × 72 = 490,000
211 × 5 × 72 = 501,760
212 × 53 = 512,000
27 × 54 × 7 = 560,000
214 × 5 × 7 = 573,440
29 × 52 × 72 = 627,200
210 × 54 = 640,000
212 × 52 × 7 = 716,800
27 × 53 × 72 = 784,000
214 × 72 = 802,816
210 × 53 × 7 = 896,000
25 × 54 × 72 = 980,000
212 × 5 × 72 = 1,003,520
213 × 53 = 1,024,000
28 × 54 × 7 = 1,120,000
210 × 52 × 72 = 1,254,400
211 × 54 = 1,280,000
213 × 52 × 7 = 1,433,600
28 × 53 × 72 = 1,568,000
211 × 53 × 7 = 1,792,000
26 × 54 × 72 = 1,960,000
213 × 5 × 72 = 2,007,040
214 × 53 = 2,048,000
29 × 54 × 7 = 2,240,000
211 × 52 × 72 = 2,508,800
212 × 54 = 2,560,000
214 × 52 × 7 = 2,867,200
29 × 53 × 72 = 3,136,000
212 × 53 × 7 = 3,584,000
27 × 54 × 72 = 3,920,000
214 × 5 × 72 = 4,014,080
210 × 54 × 7 = 4,480,000
212 × 52 × 72 = 5,017,600
213 × 54 = 5,120,000
210 × 53 × 72 = 6,272,000
213 × 53 × 7 = 7,168,000
28 × 54 × 72 = 7,840,000
211 × 54 × 7 = 8,960,000
213 × 52 × 72 = 10,035,200
214 × 54 = 10,240,000
211 × 53 × 72 = 12,544,000
214 × 53 × 7 = 14,336,000
29 × 54 × 72 = 15,680,000
212 × 54 × 7 = 17,920,000
214 × 52 × 72 = 20,070,400
212 × 53 × 72 = 25,088,000
210 × 54 × 72 = 31,360,000
213 × 54 × 7 = 35,840,000
213 × 53 × 72 = 50,176,000
211 × 54 × 72 = 62,720,000
214 × 54 × 7 = 71,680,000
214 × 53 × 72 = 100,352,000
212 × 54 × 72 = 125,440,000
213 × 54 × 72 = 250,880,000
214 × 54 × 72 = 501,760,000

The final answer:
(scroll down)

501,760,000 has 225 factors (divisors):
1; 2; 4; 5; 7; 8; 10; 14; 16; 20; 25; 28; 32; 35; 40; 49; 50; 56; 64; 70; 80; 98; 100; 112; 125; 128; 140; 160; 175; 196; 200; 224; 245; 250; 256; 280; 320; 350; 392; 400; 448; 490; 500; 512; 560; 625; 640; 700; 784; 800; 875; 896; 980; 1,000; 1,024; 1,120; 1,225; 1,250; 1,280; 1,400; 1,568; 1,600; 1,750; 1,792; 1,960; 2,000; 2,048; 2,240; 2,450; 2,500; 2,560; 2,800; 3,136; 3,200; 3,500; 3,584; 3,920; 4,000; 4,096; 4,375; 4,480; 4,900; 5,000; 5,120; 5,600; 6,125; 6,272; 6,400; 7,000; 7,168; 7,840; 8,000; 8,192; 8,750; 8,960; 9,800; 10,000; 10,240; 11,200; 12,250; 12,544; 12,800; 14,000; 14,336; 15,680; 16,000; 16,384; 17,500; 17,920; 19,600; 20,000; 20,480; 22,400; 24,500; 25,088; 25,600; 28,000; 28,672; 30,625; 31,360; 32,000; 35,000; 35,840; 39,200; 40,000; 40,960; 44,800; 49,000; 50,176; 51,200; 56,000; 57,344; 61,250; 62,720; 64,000; 70,000; 71,680; 78,400; 80,000; 81,920; 89,600; 98,000; 100,352; 102,400; 112,000; 114,688; 122,500; 125,440; 128,000; 140,000; 143,360; 156,800; 160,000; 179,200; 196,000; 200,704; 204,800; 224,000; 245,000; 250,880; 256,000; 280,000; 286,720; 313,600; 320,000; 358,400; 392,000; 401,408; 409,600; 448,000; 490,000; 501,760; 512,000; 560,000; 573,440; 627,200; 640,000; 716,800; 784,000; 802,816; 896,000; 980,000; 1,003,520; 1,024,000; 1,120,000; 1,254,400; 1,280,000; 1,433,600; 1,568,000; 1,792,000; 1,960,000; 2,007,040; 2,048,000; 2,240,000; 2,508,800; 2,560,000; 2,867,200; 3,136,000; 3,584,000; 3,920,000; 4,014,080; 4,480,000; 5,017,600; 5,120,000; 6,272,000; 7,168,000; 7,840,000; 8,960,000; 10,035,200; 10,240,000; 12,544,000; 14,336,000; 15,680,000; 17,920,000; 20,070,400; 25,088,000; 31,360,000; 35,840,000; 50,176,000; 62,720,000; 71,680,000; 100,352,000; 125,440,000; 250,880,000 and 501,760,000
out of which 3 prime factors: 2; 5 and 7
501,760,000 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 common factors:

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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".