Given the Number 22,848,000, Calculate (Find) All the Factors (All the Divisors) of the Number 22,848,000 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 22,848,000

1. Carry out the prime factorization of the number 22,848,000:

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

22,848,000 = 29 × 3 × 53 × 7 × 17
22,848,000 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 22,848,000

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
prime factor = 7
23 = 8
2 × 5 = 10
22 × 3 = 12
2 × 7 = 14
3 × 5 = 15
24 = 16
prime factor = 17
22 × 5 = 20
3 × 7 = 21
23 × 3 = 24
52 = 25
22 × 7 = 28
2 × 3 × 5 = 30
25 = 32
2 × 17 = 34
5 × 7 = 35
23 × 5 = 40
2 × 3 × 7 = 42
24 × 3 = 48
2 × 52 = 50
3 × 17 = 51
23 × 7 = 56
22 × 3 × 5 = 60
26 = 64
22 × 17 = 68
2 × 5 × 7 = 70
3 × 52 = 75
24 × 5 = 80
22 × 3 × 7 = 84
5 × 17 = 85
25 × 3 = 96
22 × 52 = 100
2 × 3 × 17 = 102
3 × 5 × 7 = 105
24 × 7 = 112
7 × 17 = 119
23 × 3 × 5 = 120
53 = 125
27 = 128
23 × 17 = 136
22 × 5 × 7 = 140
2 × 3 × 52 = 150
25 × 5 = 160
23 × 3 × 7 = 168
2 × 5 × 17 = 170
52 × 7 = 175
26 × 3 = 192
23 × 52 = 200
22 × 3 × 17 = 204
2 × 3 × 5 × 7 = 210
25 × 7 = 224
2 × 7 × 17 = 238
24 × 3 × 5 = 240
2 × 53 = 250
3 × 5 × 17 = 255
28 = 256
24 × 17 = 272
23 × 5 × 7 = 280
22 × 3 × 52 = 300
26 × 5 = 320
24 × 3 × 7 = 336
22 × 5 × 17 = 340
2 × 52 × 7 = 350
3 × 7 × 17 = 357
3 × 53 = 375
27 × 3 = 384
24 × 52 = 400
23 × 3 × 17 = 408
22 × 3 × 5 × 7 = 420
52 × 17 = 425
26 × 7 = 448
22 × 7 × 17 = 476
25 × 3 × 5 = 480
22 × 53 = 500
2 × 3 × 5 × 17 = 510
29 = 512
3 × 52 × 7 = 525
25 × 17 = 544
24 × 5 × 7 = 560
5 × 7 × 17 = 595
23 × 3 × 52 = 600
27 × 5 = 640
25 × 3 × 7 = 672
23 × 5 × 17 = 680
22 × 52 × 7 = 700
2 × 3 × 7 × 17 = 714
2 × 3 × 53 = 750
28 × 3 = 768
25 × 52 = 800
24 × 3 × 17 = 816
23 × 3 × 5 × 7 = 840
2 × 52 × 17 = 850
53 × 7 = 875
27 × 7 = 896
23 × 7 × 17 = 952
26 × 3 × 5 = 960
23 × 53 = 1,000
22 × 3 × 5 × 17 = 1,020
2 × 3 × 52 × 7 = 1,050
26 × 17 = 1,088
25 × 5 × 7 = 1,120
2 × 5 × 7 × 17 = 1,190
24 × 3 × 52 = 1,200
3 × 52 × 17 = 1,275
28 × 5 = 1,280
26 × 3 × 7 = 1,344
24 × 5 × 17 = 1,360
23 × 52 × 7 = 1,400
22 × 3 × 7 × 17 = 1,428
22 × 3 × 53 = 1,500
29 × 3 = 1,536
26 × 52 = 1,600
25 × 3 × 17 = 1,632
24 × 3 × 5 × 7 = 1,680
22 × 52 × 17 = 1,700
2 × 53 × 7 = 1,750
3 × 5 × 7 × 17 = 1,785
28 × 7 = 1,792
24 × 7 × 17 = 1,904
27 × 3 × 5 = 1,920
24 × 53 = 2,000
23 × 3 × 5 × 17 = 2,040
22 × 3 × 52 × 7 = 2,100
53 × 17 = 2,125
27 × 17 = 2,176
26 × 5 × 7 = 2,240
22 × 5 × 7 × 17 = 2,380
25 × 3 × 52 = 2,400
2 × 3 × 52 × 17 = 2,550
29 × 5 = 2,560
3 × 53 × 7 = 2,625
27 × 3 × 7 = 2,688
25 × 5 × 17 = 2,720
24 × 52 × 7 = 2,800
23 × 3 × 7 × 17 = 2,856
52 × 7 × 17 = 2,975
23 × 3 × 53 = 3,000
27 × 52 = 3,200
26 × 3 × 17 = 3,264
25 × 3 × 5 × 7 = 3,360
23 × 52 × 17 = 3,400
22 × 53 × 7 = 3,500
2 × 3 × 5 × 7 × 17 = 3,570
29 × 7 = 3,584
25 × 7 × 17 = 3,808
28 × 3 × 5 = 3,840
25 × 53 = 4,000
24 × 3 × 5 × 17 = 4,080
23 × 3 × 52 × 7 = 4,200
2 × 53 × 17 = 4,250
28 × 17 = 4,352
27 × 5 × 7 = 4,480
23 × 5 × 7 × 17 = 4,760
This list continues below...

... This list continues from above
26 × 3 × 52 = 4,800
22 × 3 × 52 × 17 = 5,100
2 × 3 × 53 × 7 = 5,250
28 × 3 × 7 = 5,376
26 × 5 × 17 = 5,440
25 × 52 × 7 = 5,600
24 × 3 × 7 × 17 = 5,712
2 × 52 × 7 × 17 = 5,950
24 × 3 × 53 = 6,000
3 × 53 × 17 = 6,375
28 × 52 = 6,400
27 × 3 × 17 = 6,528
26 × 3 × 5 × 7 = 6,720
24 × 52 × 17 = 6,800
23 × 53 × 7 = 7,000
22 × 3 × 5 × 7 × 17 = 7,140
26 × 7 × 17 = 7,616
29 × 3 × 5 = 7,680
26 × 53 = 8,000
25 × 3 × 5 × 17 = 8,160
24 × 3 × 52 × 7 = 8,400
22 × 53 × 17 = 8,500
29 × 17 = 8,704
3 × 52 × 7 × 17 = 8,925
28 × 5 × 7 = 8,960
24 × 5 × 7 × 17 = 9,520
27 × 3 × 52 = 9,600
23 × 3 × 52 × 17 = 10,200
22 × 3 × 53 × 7 = 10,500
29 × 3 × 7 = 10,752
27 × 5 × 17 = 10,880
26 × 52 × 7 = 11,200
25 × 3 × 7 × 17 = 11,424
22 × 52 × 7 × 17 = 11,900
25 × 3 × 53 = 12,000
2 × 3 × 53 × 17 = 12,750
29 × 52 = 12,800
28 × 3 × 17 = 13,056
27 × 3 × 5 × 7 = 13,440
25 × 52 × 17 = 13,600
24 × 53 × 7 = 14,000
23 × 3 × 5 × 7 × 17 = 14,280
53 × 7 × 17 = 14,875
27 × 7 × 17 = 15,232
27 × 53 = 16,000
26 × 3 × 5 × 17 = 16,320
25 × 3 × 52 × 7 = 16,800
23 × 53 × 17 = 17,000
2 × 3 × 52 × 7 × 17 = 17,850
29 × 5 × 7 = 17,920
25 × 5 × 7 × 17 = 19,040
28 × 3 × 52 = 19,200
24 × 3 × 52 × 17 = 20,400
23 × 3 × 53 × 7 = 21,000
28 × 5 × 17 = 21,760
27 × 52 × 7 = 22,400
26 × 3 × 7 × 17 = 22,848
23 × 52 × 7 × 17 = 23,800
26 × 3 × 53 = 24,000
22 × 3 × 53 × 17 = 25,500
29 × 3 × 17 = 26,112
28 × 3 × 5 × 7 = 26,880
26 × 52 × 17 = 27,200
25 × 53 × 7 = 28,000
24 × 3 × 5 × 7 × 17 = 28,560
2 × 53 × 7 × 17 = 29,750
28 × 7 × 17 = 30,464
28 × 53 = 32,000
27 × 3 × 5 × 17 = 32,640
26 × 3 × 52 × 7 = 33,600
24 × 53 × 17 = 34,000
22 × 3 × 52 × 7 × 17 = 35,700
26 × 5 × 7 × 17 = 38,080
29 × 3 × 52 = 38,400
25 × 3 × 52 × 17 = 40,800
24 × 3 × 53 × 7 = 42,000
29 × 5 × 17 = 43,520
3 × 53 × 7 × 17 = 44,625
28 × 52 × 7 = 44,800
27 × 3 × 7 × 17 = 45,696
24 × 52 × 7 × 17 = 47,600
27 × 3 × 53 = 48,000
23 × 3 × 53 × 17 = 51,000
29 × 3 × 5 × 7 = 53,760
27 × 52 × 17 = 54,400
26 × 53 × 7 = 56,000
25 × 3 × 5 × 7 × 17 = 57,120
22 × 53 × 7 × 17 = 59,500
29 × 7 × 17 = 60,928
29 × 53 = 64,000
28 × 3 × 5 × 17 = 65,280
27 × 3 × 52 × 7 = 67,200
25 × 53 × 17 = 68,000
23 × 3 × 52 × 7 × 17 = 71,400
27 × 5 × 7 × 17 = 76,160
26 × 3 × 52 × 17 = 81,600
25 × 3 × 53 × 7 = 84,000
2 × 3 × 53 × 7 × 17 = 89,250
29 × 52 × 7 = 89,600
28 × 3 × 7 × 17 = 91,392
25 × 52 × 7 × 17 = 95,200
28 × 3 × 53 = 96,000
24 × 3 × 53 × 17 = 102,000
28 × 52 × 17 = 108,800
27 × 53 × 7 = 112,000
26 × 3 × 5 × 7 × 17 = 114,240
23 × 53 × 7 × 17 = 119,000
29 × 3 × 5 × 17 = 130,560
28 × 3 × 52 × 7 = 134,400
26 × 53 × 17 = 136,000
24 × 3 × 52 × 7 × 17 = 142,800
28 × 5 × 7 × 17 = 152,320
27 × 3 × 52 × 17 = 163,200
26 × 3 × 53 × 7 = 168,000
22 × 3 × 53 × 7 × 17 = 178,500
29 × 3 × 7 × 17 = 182,784
26 × 52 × 7 × 17 = 190,400
29 × 3 × 53 = 192,000
25 × 3 × 53 × 17 = 204,000
29 × 52 × 17 = 217,600
28 × 53 × 7 = 224,000
27 × 3 × 5 × 7 × 17 = 228,480
24 × 53 × 7 × 17 = 238,000
29 × 3 × 52 × 7 = 268,800
27 × 53 × 17 = 272,000
25 × 3 × 52 × 7 × 17 = 285,600
29 × 5 × 7 × 17 = 304,640
28 × 3 × 52 × 17 = 326,400
27 × 3 × 53 × 7 = 336,000
23 × 3 × 53 × 7 × 17 = 357,000
27 × 52 × 7 × 17 = 380,800
26 × 3 × 53 × 17 = 408,000
29 × 53 × 7 = 448,000
28 × 3 × 5 × 7 × 17 = 456,960
25 × 53 × 7 × 17 = 476,000
28 × 53 × 17 = 544,000
26 × 3 × 52 × 7 × 17 = 571,200
29 × 3 × 52 × 17 = 652,800
28 × 3 × 53 × 7 = 672,000
24 × 3 × 53 × 7 × 17 = 714,000
28 × 52 × 7 × 17 = 761,600
27 × 3 × 53 × 17 = 816,000
29 × 3 × 5 × 7 × 17 = 913,920
26 × 53 × 7 × 17 = 952,000
29 × 53 × 17 = 1,088,000
27 × 3 × 52 × 7 × 17 = 1,142,400
29 × 3 × 53 × 7 = 1,344,000
25 × 3 × 53 × 7 × 17 = 1,428,000
29 × 52 × 7 × 17 = 1,523,200
28 × 3 × 53 × 17 = 1,632,000
27 × 53 × 7 × 17 = 1,904,000
28 × 3 × 52 × 7 × 17 = 2,284,800
26 × 3 × 53 × 7 × 17 = 2,856,000
29 × 3 × 53 × 17 = 3,264,000
28 × 53 × 7 × 17 = 3,808,000
29 × 3 × 52 × 7 × 17 = 4,569,600
27 × 3 × 53 × 7 × 17 = 5,712,000
29 × 53 × 7 × 17 = 7,616,000
28 × 3 × 53 × 7 × 17 = 11,424,000
29 × 3 × 53 × 7 × 17 = 22,848,000

The final answer:
(scroll down)

22,848,000 has 320 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 8; 10; 12; 14; 15; 16; 17; 20; 21; 24; 25; 28; 30; 32; 34; 35; 40; 42; 48; 50; 51; 56; 60; 64; 68; 70; 75; 80; 84; 85; 96; 100; 102; 105; 112; 119; 120; 125; 128; 136; 140; 150; 160; 168; 170; 175; 192; 200; 204; 210; 224; 238; 240; 250; 255; 256; 272; 280; 300; 320; 336; 340; 350; 357; 375; 384; 400; 408; 420; 425; 448; 476; 480; 500; 510; 512; 525; 544; 560; 595; 600; 640; 672; 680; 700; 714; 750; 768; 800; 816; 840; 850; 875; 896; 952; 960; 1,000; 1,020; 1,050; 1,088; 1,120; 1,190; 1,200; 1,275; 1,280; 1,344; 1,360; 1,400; 1,428; 1,500; 1,536; 1,600; 1,632; 1,680; 1,700; 1,750; 1,785; 1,792; 1,904; 1,920; 2,000; 2,040; 2,100; 2,125; 2,176; 2,240; 2,380; 2,400; 2,550; 2,560; 2,625; 2,688; 2,720; 2,800; 2,856; 2,975; 3,000; 3,200; 3,264; 3,360; 3,400; 3,500; 3,570; 3,584; 3,808; 3,840; 4,000; 4,080; 4,200; 4,250; 4,352; 4,480; 4,760; 4,800; 5,100; 5,250; 5,376; 5,440; 5,600; 5,712; 5,950; 6,000; 6,375; 6,400; 6,528; 6,720; 6,800; 7,000; 7,140; 7,616; 7,680; 8,000; 8,160; 8,400; 8,500; 8,704; 8,925; 8,960; 9,520; 9,600; 10,200; 10,500; 10,752; 10,880; 11,200; 11,424; 11,900; 12,000; 12,750; 12,800; 13,056; 13,440; 13,600; 14,000; 14,280; 14,875; 15,232; 16,000; 16,320; 16,800; 17,000; 17,850; 17,920; 19,040; 19,200; 20,400; 21,000; 21,760; 22,400; 22,848; 23,800; 24,000; 25,500; 26,112; 26,880; 27,200; 28,000; 28,560; 29,750; 30,464; 32,000; 32,640; 33,600; 34,000; 35,700; 38,080; 38,400; 40,800; 42,000; 43,520; 44,625; 44,800; 45,696; 47,600; 48,000; 51,000; 53,760; 54,400; 56,000; 57,120; 59,500; 60,928; 64,000; 65,280; 67,200; 68,000; 71,400; 76,160; 81,600; 84,000; 89,250; 89,600; 91,392; 95,200; 96,000; 102,000; 108,800; 112,000; 114,240; 119,000; 130,560; 134,400; 136,000; 142,800; 152,320; 163,200; 168,000; 178,500; 182,784; 190,400; 192,000; 204,000; 217,600; 224,000; 228,480; 238,000; 268,800; 272,000; 285,600; 304,640; 326,400; 336,000; 357,000; 380,800; 408,000; 448,000; 456,960; 476,000; 544,000; 571,200; 652,800; 672,000; 714,000; 761,600; 816,000; 913,920; 952,000; 1,088,000; 1,142,400; 1,344,000; 1,428,000; 1,523,200; 1,632,000; 1,904,000; 2,284,800; 2,856,000; 3,264,000; 3,808,000; 4,569,600; 5,712,000; 7,616,000; 11,424,000 and 22,848,000
out of which 5 prime factors: 2; 3; 5; 7 and 17
22,848,000 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 22,847,998?

» What are all the proper, improper and prime factors (divisors) of the number 22,848,011?


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".