Given the Number 23,919,000, Calculate (Find) All the Factors (All the Divisors) of the Number 23,919,000 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 23,919,000

1. Carry out the prime factorization of the number 23,919,000:

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

23,919,000 = 23 × 3 × 53 × 7 × 17 × 67
23,919,000 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 23,919,000

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
prime factor = 17
22 × 5 = 20
3 × 7 = 21
23 × 3 = 24
52 = 25
22 × 7 = 28
2 × 3 × 5 = 30
2 × 17 = 34
5 × 7 = 35
23 × 5 = 40
2 × 3 × 7 = 42
2 × 52 = 50
3 × 17 = 51
23 × 7 = 56
22 × 3 × 5 = 60
prime factor = 67
22 × 17 = 68
2 × 5 × 7 = 70
3 × 52 = 75
22 × 3 × 7 = 84
5 × 17 = 85
22 × 52 = 100
2 × 3 × 17 = 102
3 × 5 × 7 = 105
7 × 17 = 119
23 × 3 × 5 = 120
53 = 125
2 × 67 = 134
23 × 17 = 136
22 × 5 × 7 = 140
2 × 3 × 52 = 150
23 × 3 × 7 = 168
2 × 5 × 17 = 170
52 × 7 = 175
23 × 52 = 200
3 × 67 = 201
22 × 3 × 17 = 204
2 × 3 × 5 × 7 = 210
2 × 7 × 17 = 238
2 × 53 = 250
3 × 5 × 17 = 255
22 × 67 = 268
23 × 5 × 7 = 280
22 × 3 × 52 = 300
5 × 67 = 335
22 × 5 × 17 = 340
2 × 52 × 7 = 350
3 × 7 × 17 = 357
3 × 53 = 375
2 × 3 × 67 = 402
23 × 3 × 17 = 408
22 × 3 × 5 × 7 = 420
52 × 17 = 425
7 × 67 = 469
22 × 7 × 17 = 476
22 × 53 = 500
2 × 3 × 5 × 17 = 510
3 × 52 × 7 = 525
23 × 67 = 536
5 × 7 × 17 = 595
23 × 3 × 52 = 600
2 × 5 × 67 = 670
23 × 5 × 17 = 680
22 × 52 × 7 = 700
2 × 3 × 7 × 17 = 714
2 × 3 × 53 = 750
22 × 3 × 67 = 804
23 × 3 × 5 × 7 = 840
2 × 52 × 17 = 850
53 × 7 = 875
2 × 7 × 67 = 938
23 × 7 × 17 = 952
23 × 53 = 1,000
3 × 5 × 67 = 1,005
22 × 3 × 5 × 17 = 1,020
2 × 3 × 52 × 7 = 1,050
17 × 67 = 1,139
2 × 5 × 7 × 17 = 1,190
3 × 52 × 17 = 1,275
22 × 5 × 67 = 1,340
23 × 52 × 7 = 1,400
3 × 7 × 67 = 1,407
22 × 3 × 7 × 17 = 1,428
22 × 3 × 53 = 1,500
23 × 3 × 67 = 1,608
52 × 67 = 1,675
22 × 52 × 17 = 1,700
2 × 53 × 7 = 1,750
3 × 5 × 7 × 17 = 1,785
22 × 7 × 67 = 1,876
2 × 3 × 5 × 67 = 2,010
23 × 3 × 5 × 17 = 2,040
22 × 3 × 52 × 7 = 2,100
53 × 17 = 2,125
2 × 17 × 67 = 2,278
5 × 7 × 67 = 2,345
22 × 5 × 7 × 17 = 2,380
2 × 3 × 52 × 17 = 2,550
3 × 53 × 7 = 2,625
23 × 5 × 67 = 2,680
2 × 3 × 7 × 67 = 2,814
23 × 3 × 7 × 17 = 2,856
52 × 7 × 17 = 2,975
23 × 3 × 53 = 3,000
2 × 52 × 67 = 3,350
23 × 52 × 17 = 3,400
3 × 17 × 67 = 3,417
22 × 53 × 7 = 3,500
2 × 3 × 5 × 7 × 17 = 3,570
23 × 7 × 67 = 3,752
22 × 3 × 5 × 67 = 4,020
23 × 3 × 52 × 7 = 4,200
2 × 53 × 17 = 4,250
22 × 17 × 67 = 4,556
2 × 5 × 7 × 67 = 4,690
23 × 5 × 7 × 17 = 4,760
This list continues below...

... This list continues from above
3 × 52 × 67 = 5,025
22 × 3 × 52 × 17 = 5,100
2 × 3 × 53 × 7 = 5,250
22 × 3 × 7 × 67 = 5,628
5 × 17 × 67 = 5,695
2 × 52 × 7 × 17 = 5,950
3 × 53 × 17 = 6,375
22 × 52 × 67 = 6,700
2 × 3 × 17 × 67 = 6,834
23 × 53 × 7 = 7,000
3 × 5 × 7 × 67 = 7,035
22 × 3 × 5 × 7 × 17 = 7,140
7 × 17 × 67 = 7,973
23 × 3 × 5 × 67 = 8,040
53 × 67 = 8,375
22 × 53 × 17 = 8,500
3 × 52 × 7 × 17 = 8,925
23 × 17 × 67 = 9,112
22 × 5 × 7 × 67 = 9,380
2 × 3 × 52 × 67 = 10,050
23 × 3 × 52 × 17 = 10,200
22 × 3 × 53 × 7 = 10,500
23 × 3 × 7 × 67 = 11,256
2 × 5 × 17 × 67 = 11,390
52 × 7 × 67 = 11,725
22 × 52 × 7 × 17 = 11,900
2 × 3 × 53 × 17 = 12,750
23 × 52 × 67 = 13,400
22 × 3 × 17 × 67 = 13,668
2 × 3 × 5 × 7 × 67 = 14,070
23 × 3 × 5 × 7 × 17 = 14,280
53 × 7 × 17 = 14,875
2 × 7 × 17 × 67 = 15,946
2 × 53 × 67 = 16,750
23 × 53 × 17 = 17,000
3 × 5 × 17 × 67 = 17,085
2 × 3 × 52 × 7 × 17 = 17,850
23 × 5 × 7 × 67 = 18,760
22 × 3 × 52 × 67 = 20,100
23 × 3 × 53 × 7 = 21,000
22 × 5 × 17 × 67 = 22,780
2 × 52 × 7 × 67 = 23,450
23 × 52 × 7 × 17 = 23,800
3 × 7 × 17 × 67 = 23,919
3 × 53 × 67 = 25,125
22 × 3 × 53 × 17 = 25,500
23 × 3 × 17 × 67 = 27,336
22 × 3 × 5 × 7 × 67 = 28,140
52 × 17 × 67 = 28,475
2 × 53 × 7 × 17 = 29,750
22 × 7 × 17 × 67 = 31,892
22 × 53 × 67 = 33,500
2 × 3 × 5 × 17 × 67 = 34,170
3 × 52 × 7 × 67 = 35,175
22 × 3 × 52 × 7 × 17 = 35,700
5 × 7 × 17 × 67 = 39,865
23 × 3 × 52 × 67 = 40,200
3 × 53 × 7 × 17 = 44,625
23 × 5 × 17 × 67 = 45,560
22 × 52 × 7 × 67 = 46,900
2 × 3 × 7 × 17 × 67 = 47,838
2 × 3 × 53 × 67 = 50,250
23 × 3 × 53 × 17 = 51,000
23 × 3 × 5 × 7 × 67 = 56,280
2 × 52 × 17 × 67 = 56,950
53 × 7 × 67 = 58,625
22 × 53 × 7 × 17 = 59,500
23 × 7 × 17 × 67 = 63,784
23 × 53 × 67 = 67,000
22 × 3 × 5 × 17 × 67 = 68,340
2 × 3 × 52 × 7 × 67 = 70,350
23 × 3 × 52 × 7 × 17 = 71,400
2 × 5 × 7 × 17 × 67 = 79,730
3 × 52 × 17 × 67 = 85,425
2 × 3 × 53 × 7 × 17 = 89,250
23 × 52 × 7 × 67 = 93,800
22 × 3 × 7 × 17 × 67 = 95,676
22 × 3 × 53 × 67 = 100,500
22 × 52 × 17 × 67 = 113,900
2 × 53 × 7 × 67 = 117,250
23 × 53 × 7 × 17 = 119,000
3 × 5 × 7 × 17 × 67 = 119,595
23 × 3 × 5 × 17 × 67 = 136,680
22 × 3 × 52 × 7 × 67 = 140,700
53 × 17 × 67 = 142,375
22 × 5 × 7 × 17 × 67 = 159,460
2 × 3 × 52 × 17 × 67 = 170,850
3 × 53 × 7 × 67 = 175,875
22 × 3 × 53 × 7 × 17 = 178,500
23 × 3 × 7 × 17 × 67 = 191,352
52 × 7 × 17 × 67 = 199,325
23 × 3 × 53 × 67 = 201,000
23 × 52 × 17 × 67 = 227,800
22 × 53 × 7 × 67 = 234,500
2 × 3 × 5 × 7 × 17 × 67 = 239,190
23 × 3 × 52 × 7 × 67 = 281,400
2 × 53 × 17 × 67 = 284,750
23 × 5 × 7 × 17 × 67 = 318,920
22 × 3 × 52 × 17 × 67 = 341,700
2 × 3 × 53 × 7 × 67 = 351,750
23 × 3 × 53 × 7 × 17 = 357,000
2 × 52 × 7 × 17 × 67 = 398,650
3 × 53 × 17 × 67 = 427,125
23 × 53 × 7 × 67 = 469,000
22 × 3 × 5 × 7 × 17 × 67 = 478,380
22 × 53 × 17 × 67 = 569,500
3 × 52 × 7 × 17 × 67 = 597,975
23 × 3 × 52 × 17 × 67 = 683,400
22 × 3 × 53 × 7 × 67 = 703,500
22 × 52 × 7 × 17 × 67 = 797,300
2 × 3 × 53 × 17 × 67 = 854,250
23 × 3 × 5 × 7 × 17 × 67 = 956,760
53 × 7 × 17 × 67 = 996,625
23 × 53 × 17 × 67 = 1,139,000
2 × 3 × 52 × 7 × 17 × 67 = 1,195,950
23 × 3 × 53 × 7 × 67 = 1,407,000
23 × 52 × 7 × 17 × 67 = 1,594,600
22 × 3 × 53 × 17 × 67 = 1,708,500
2 × 53 × 7 × 17 × 67 = 1,993,250
22 × 3 × 52 × 7 × 17 × 67 = 2,391,900
3 × 53 × 7 × 17 × 67 = 2,989,875
23 × 3 × 53 × 17 × 67 = 3,417,000
22 × 53 × 7 × 17 × 67 = 3,986,500
23 × 3 × 52 × 7 × 17 × 67 = 4,783,800
2 × 3 × 53 × 7 × 17 × 67 = 5,979,750
23 × 53 × 7 × 17 × 67 = 7,973,000
22 × 3 × 53 × 7 × 17 × 67 = 11,959,500
23 × 3 × 53 × 7 × 17 × 67 = 23,919,000

The final answer:
(scroll down)

23,919,000 has 256 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 8; 10; 12; 14; 15; 17; 20; 21; 24; 25; 28; 30; 34; 35; 40; 42; 50; 51; 56; 60; 67; 68; 70; 75; 84; 85; 100; 102; 105; 119; 120; 125; 134; 136; 140; 150; 168; 170; 175; 200; 201; 204; 210; 238; 250; 255; 268; 280; 300; 335; 340; 350; 357; 375; 402; 408; 420; 425; 469; 476; 500; 510; 525; 536; 595; 600; 670; 680; 700; 714; 750; 804; 840; 850; 875; 938; 952; 1,000; 1,005; 1,020; 1,050; 1,139; 1,190; 1,275; 1,340; 1,400; 1,407; 1,428; 1,500; 1,608; 1,675; 1,700; 1,750; 1,785; 1,876; 2,010; 2,040; 2,100; 2,125; 2,278; 2,345; 2,380; 2,550; 2,625; 2,680; 2,814; 2,856; 2,975; 3,000; 3,350; 3,400; 3,417; 3,500; 3,570; 3,752; 4,020; 4,200; 4,250; 4,556; 4,690; 4,760; 5,025; 5,100; 5,250; 5,628; 5,695; 5,950; 6,375; 6,700; 6,834; 7,000; 7,035; 7,140; 7,973; 8,040; 8,375; 8,500; 8,925; 9,112; 9,380; 10,050; 10,200; 10,500; 11,256; 11,390; 11,725; 11,900; 12,750; 13,400; 13,668; 14,070; 14,280; 14,875; 15,946; 16,750; 17,000; 17,085; 17,850; 18,760; 20,100; 21,000; 22,780; 23,450; 23,800; 23,919; 25,125; 25,500; 27,336; 28,140; 28,475; 29,750; 31,892; 33,500; 34,170; 35,175; 35,700; 39,865; 40,200; 44,625; 45,560; 46,900; 47,838; 50,250; 51,000; 56,280; 56,950; 58,625; 59,500; 63,784; 67,000; 68,340; 70,350; 71,400; 79,730; 85,425; 89,250; 93,800; 95,676; 100,500; 113,900; 117,250; 119,000; 119,595; 136,680; 140,700; 142,375; 159,460; 170,850; 175,875; 178,500; 191,352; 199,325; 201,000; 227,800; 234,500; 239,190; 281,400; 284,750; 318,920; 341,700; 351,750; 357,000; 398,650; 427,125; 469,000; 478,380; 569,500; 597,975; 683,400; 703,500; 797,300; 854,250; 956,760; 996,625; 1,139,000; 1,195,950; 1,407,000; 1,594,600; 1,708,500; 1,993,250; 2,391,900; 2,989,875; 3,417,000; 3,986,500; 4,783,800; 5,979,750; 7,973,000; 11,959,500 and 23,919,000
out of which 6 prime factors: 2; 3; 5; 7; 17 and 67
23,919,000 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 23,918,991?

» What are all the proper, improper and prime factors (divisors) of the number 23,919,007?


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.

The latest 10 sets of calculated factors (divisors): of one number or the common factors of two numbers

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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".