Given the Number 12,345,060, Calculate (Find) All the Factors (All the Divisors) of the Number 12,345,060 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 12,345,060

1. Carry out the prime factorization of the number 12,345,060:

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

12,345,060 = 22 × 3 × 5 × 72 × 13 × 17 × 19
12,345,060 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 12,345,060

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
2 × 5 = 10
22 × 3 = 12
prime factor = 13
2 × 7 = 14
3 × 5 = 15
prime factor = 17
prime factor = 19
22 × 5 = 20
3 × 7 = 21
2 × 13 = 26
22 × 7 = 28
2 × 3 × 5 = 30
2 × 17 = 34
5 × 7 = 35
2 × 19 = 38
3 × 13 = 39
2 × 3 × 7 = 42
72 = 49
3 × 17 = 51
22 × 13 = 52
3 × 19 = 57
22 × 3 × 5 = 60
5 × 13 = 65
22 × 17 = 68
2 × 5 × 7 = 70
22 × 19 = 76
2 × 3 × 13 = 78
22 × 3 × 7 = 84
5 × 17 = 85
7 × 13 = 91
5 × 19 = 95
2 × 72 = 98
2 × 3 × 17 = 102
3 × 5 × 7 = 105
2 × 3 × 19 = 114
7 × 17 = 119
2 × 5 × 13 = 130
7 × 19 = 133
22 × 5 × 7 = 140
3 × 72 = 147
22 × 3 × 13 = 156
2 × 5 × 17 = 170
2 × 7 × 13 = 182
2 × 5 × 19 = 190
3 × 5 × 13 = 195
22 × 72 = 196
22 × 3 × 17 = 204
2 × 3 × 5 × 7 = 210
13 × 17 = 221
22 × 3 × 19 = 228
2 × 7 × 17 = 238
5 × 72 = 245
13 × 19 = 247
3 × 5 × 17 = 255
22 × 5 × 13 = 260
2 × 7 × 19 = 266
3 × 7 × 13 = 273
3 × 5 × 19 = 285
2 × 3 × 72 = 294
17 × 19 = 323
22 × 5 × 17 = 340
3 × 7 × 17 = 357
22 × 7 × 13 = 364
22 × 5 × 19 = 380
2 × 3 × 5 × 13 = 390
3 × 7 × 19 = 399
22 × 3 × 5 × 7 = 420
2 × 13 × 17 = 442
5 × 7 × 13 = 455
22 × 7 × 17 = 476
2 × 5 × 72 = 490
2 × 13 × 19 = 494
2 × 3 × 5 × 17 = 510
22 × 7 × 19 = 532
2 × 3 × 7 × 13 = 546
2 × 3 × 5 × 19 = 570
22 × 3 × 72 = 588
5 × 7 × 17 = 595
72 × 13 = 637
2 × 17 × 19 = 646
3 × 13 × 17 = 663
5 × 7 × 19 = 665
2 × 3 × 7 × 17 = 714
3 × 5 × 72 = 735
3 × 13 × 19 = 741
22 × 3 × 5 × 13 = 780
2 × 3 × 7 × 19 = 798
72 × 17 = 833
22 × 13 × 17 = 884
2 × 5 × 7 × 13 = 910
72 × 19 = 931
3 × 17 × 19 = 969
22 × 5 × 72 = 980
22 × 13 × 19 = 988
22 × 3 × 5 × 17 = 1,020
22 × 3 × 7 × 13 = 1,092
5 × 13 × 17 = 1,105
22 × 3 × 5 × 19 = 1,140
2 × 5 × 7 × 17 = 1,190
5 × 13 × 19 = 1,235
2 × 72 × 13 = 1,274
22 × 17 × 19 = 1,292
2 × 3 × 13 × 17 = 1,326
2 × 5 × 7 × 19 = 1,330
3 × 5 × 7 × 13 = 1,365
22 × 3 × 7 × 17 = 1,428
2 × 3 × 5 × 72 = 1,470
2 × 3 × 13 × 19 = 1,482
7 × 13 × 17 = 1,547
22 × 3 × 7 × 19 = 1,596
5 × 17 × 19 = 1,615
2 × 72 × 17 = 1,666
7 × 13 × 19 = 1,729
3 × 5 × 7 × 17 = 1,785
22 × 5 × 7 × 13 = 1,820
2 × 72 × 19 = 1,862
3 × 72 × 13 = 1,911
2 × 3 × 17 × 19 = 1,938
3 × 5 × 7 × 19 = 1,995
2 × 5 × 13 × 17 = 2,210
7 × 17 × 19 = 2,261
22 × 5 × 7 × 17 = 2,380
2 × 5 × 13 × 19 = 2,470
3 × 72 × 17 = 2,499
22 × 72 × 13 = 2,548
22 × 3 × 13 × 17 = 2,652
22 × 5 × 7 × 19 = 2,660
2 × 3 × 5 × 7 × 13 = 2,730
3 × 72 × 19 = 2,793
22 × 3 × 5 × 72 = 2,940
22 × 3 × 13 × 19 = 2,964
2 × 7 × 13 × 17 = 3,094
5 × 72 × 13 = 3,185
2 × 5 × 17 × 19 = 3,230
3 × 5 × 13 × 17 = 3,315
22 × 72 × 17 = 3,332
2 × 7 × 13 × 19 = 3,458
This list continues below...

... This list continues from above
2 × 3 × 5 × 7 × 17 = 3,570
3 × 5 × 13 × 19 = 3,705
22 × 72 × 19 = 3,724
2 × 3 × 72 × 13 = 3,822
22 × 3 × 17 × 19 = 3,876
2 × 3 × 5 × 7 × 19 = 3,990
5 × 72 × 17 = 4,165
13 × 17 × 19 = 4,199
22 × 5 × 13 × 17 = 4,420
2 × 7 × 17 × 19 = 4,522
3 × 7 × 13 × 17 = 4,641
5 × 72 × 19 = 4,655
3 × 5 × 17 × 19 = 4,845
22 × 5 × 13 × 19 = 4,940
2 × 3 × 72 × 17 = 4,998
3 × 7 × 13 × 19 = 5,187
22 × 3 × 5 × 7 × 13 = 5,460
2 × 3 × 72 × 19 = 5,586
22 × 7 × 13 × 17 = 6,188
2 × 5 × 72 × 13 = 6,370
22 × 5 × 17 × 19 = 6,460
2 × 3 × 5 × 13 × 17 = 6,630
3 × 7 × 17 × 19 = 6,783
22 × 7 × 13 × 19 = 6,916
22 × 3 × 5 × 7 × 17 = 7,140
2 × 3 × 5 × 13 × 19 = 7,410
22 × 3 × 72 × 13 = 7,644
5 × 7 × 13 × 17 = 7,735
22 × 3 × 5 × 7 × 19 = 7,980
2 × 5 × 72 × 17 = 8,330
2 × 13 × 17 × 19 = 8,398
5 × 7 × 13 × 19 = 8,645
22 × 7 × 17 × 19 = 9,044
2 × 3 × 7 × 13 × 17 = 9,282
2 × 5 × 72 × 19 = 9,310
3 × 5 × 72 × 13 = 9,555
2 × 3 × 5 × 17 × 19 = 9,690
22 × 3 × 72 × 17 = 9,996
2 × 3 × 7 × 13 × 19 = 10,374
72 × 13 × 17 = 10,829
22 × 3 × 72 × 19 = 11,172
5 × 7 × 17 × 19 = 11,305
72 × 13 × 19 = 12,103
3 × 5 × 72 × 17 = 12,495
3 × 13 × 17 × 19 = 12,597
22 × 5 × 72 × 13 = 12,740
22 × 3 × 5 × 13 × 17 = 13,260
2 × 3 × 7 × 17 × 19 = 13,566
3 × 5 × 72 × 19 = 13,965
22 × 3 × 5 × 13 × 19 = 14,820
2 × 5 × 7 × 13 × 17 = 15,470
72 × 17 × 19 = 15,827
22 × 5 × 72 × 17 = 16,660
22 × 13 × 17 × 19 = 16,796
2 × 5 × 7 × 13 × 19 = 17,290
22 × 3 × 7 × 13 × 17 = 18,564
22 × 5 × 72 × 19 = 18,620
2 × 3 × 5 × 72 × 13 = 19,110
22 × 3 × 5 × 17 × 19 = 19,380
22 × 3 × 7 × 13 × 19 = 20,748
5 × 13 × 17 × 19 = 20,995
2 × 72 × 13 × 17 = 21,658
2 × 5 × 7 × 17 × 19 = 22,610
3 × 5 × 7 × 13 × 17 = 23,205
2 × 72 × 13 × 19 = 24,206
2 × 3 × 5 × 72 × 17 = 24,990
2 × 3 × 13 × 17 × 19 = 25,194
3 × 5 × 7 × 13 × 19 = 25,935
22 × 3 × 7 × 17 × 19 = 27,132
2 × 3 × 5 × 72 × 19 = 27,930
7 × 13 × 17 × 19 = 29,393
22 × 5 × 7 × 13 × 17 = 30,940
2 × 72 × 17 × 19 = 31,654
3 × 72 × 13 × 17 = 32,487
3 × 5 × 7 × 17 × 19 = 33,915
22 × 5 × 7 × 13 × 19 = 34,580
3 × 72 × 13 × 19 = 36,309
22 × 3 × 5 × 72 × 13 = 38,220
2 × 5 × 13 × 17 × 19 = 41,990
22 × 72 × 13 × 17 = 43,316
22 × 5 × 7 × 17 × 19 = 45,220
2 × 3 × 5 × 7 × 13 × 17 = 46,410
3 × 72 × 17 × 19 = 47,481
22 × 72 × 13 × 19 = 48,412
22 × 3 × 5 × 72 × 17 = 49,980
22 × 3 × 13 × 17 × 19 = 50,388
2 × 3 × 5 × 7 × 13 × 19 = 51,870
5 × 72 × 13 × 17 = 54,145
22 × 3 × 5 × 72 × 19 = 55,860
2 × 7 × 13 × 17 × 19 = 58,786
5 × 72 × 13 × 19 = 60,515
3 × 5 × 13 × 17 × 19 = 62,985
22 × 72 × 17 × 19 = 63,308
2 × 3 × 72 × 13 × 17 = 64,974
2 × 3 × 5 × 7 × 17 × 19 = 67,830
2 × 3 × 72 × 13 × 19 = 72,618
5 × 72 × 17 × 19 = 79,135
22 × 5 × 13 × 17 × 19 = 83,980
3 × 7 × 13 × 17 × 19 = 88,179
22 × 3 × 5 × 7 × 13 × 17 = 92,820
2 × 3 × 72 × 17 × 19 = 94,962
22 × 3 × 5 × 7 × 13 × 19 = 103,740
2 × 5 × 72 × 13 × 17 = 108,290
22 × 7 × 13 × 17 × 19 = 117,572
2 × 5 × 72 × 13 × 19 = 121,030
2 × 3 × 5 × 13 × 17 × 19 = 125,970
22 × 3 × 72 × 13 × 17 = 129,948
22 × 3 × 5 × 7 × 17 × 19 = 135,660
22 × 3 × 72 × 13 × 19 = 145,236
5 × 7 × 13 × 17 × 19 = 146,965
2 × 5 × 72 × 17 × 19 = 158,270
3 × 5 × 72 × 13 × 17 = 162,435
2 × 3 × 7 × 13 × 17 × 19 = 176,358
3 × 5 × 72 × 13 × 19 = 181,545
22 × 3 × 72 × 17 × 19 = 189,924
72 × 13 × 17 × 19 = 205,751
22 × 5 × 72 × 13 × 17 = 216,580
3 × 5 × 72 × 17 × 19 = 237,405
22 × 5 × 72 × 13 × 19 = 242,060
22 × 3 × 5 × 13 × 17 × 19 = 251,940
2 × 5 × 7 × 13 × 17 × 19 = 293,930
22 × 5 × 72 × 17 × 19 = 316,540
2 × 3 × 5 × 72 × 13 × 17 = 324,870
22 × 3 × 7 × 13 × 17 × 19 = 352,716
2 × 3 × 5 × 72 × 13 × 19 = 363,090
2 × 72 × 13 × 17 × 19 = 411,502
3 × 5 × 7 × 13 × 17 × 19 = 440,895
2 × 3 × 5 × 72 × 17 × 19 = 474,810
22 × 5 × 7 × 13 × 17 × 19 = 587,860
3 × 72 × 13 × 17 × 19 = 617,253
22 × 3 × 5 × 72 × 13 × 17 = 649,740
22 × 3 × 5 × 72 × 13 × 19 = 726,180
22 × 72 × 13 × 17 × 19 = 823,004
2 × 3 × 5 × 7 × 13 × 17 × 19 = 881,790
22 × 3 × 5 × 72 × 17 × 19 = 949,620
5 × 72 × 13 × 17 × 19 = 1,028,755
2 × 3 × 72 × 13 × 17 × 19 = 1,234,506
22 × 3 × 5 × 7 × 13 × 17 × 19 = 1,763,580
2 × 5 × 72 × 13 × 17 × 19 = 2,057,510
22 × 3 × 72 × 13 × 17 × 19 = 2,469,012
3 × 5 × 72 × 13 × 17 × 19 = 3,086,265
22 × 5 × 72 × 13 × 17 × 19 = 4,115,020
2 × 3 × 5 × 72 × 13 × 17 × 19 = 6,172,530
22 × 3 × 5 × 72 × 13 × 17 × 19 = 12,345,060

The final answer:
(scroll down)

12,345,060 has 288 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 10; 12; 13; 14; 15; 17; 19; 20; 21; 26; 28; 30; 34; 35; 38; 39; 42; 49; 51; 52; 57; 60; 65; 68; 70; 76; 78; 84; 85; 91; 95; 98; 102; 105; 114; 119; 130; 133; 140; 147; 156; 170; 182; 190; 195; 196; 204; 210; 221; 228; 238; 245; 247; 255; 260; 266; 273; 285; 294; 323; 340; 357; 364; 380; 390; 399; 420; 442; 455; 476; 490; 494; 510; 532; 546; 570; 588; 595; 637; 646; 663; 665; 714; 735; 741; 780; 798; 833; 884; 910; 931; 969; 980; 988; 1,020; 1,092; 1,105; 1,140; 1,190; 1,235; 1,274; 1,292; 1,326; 1,330; 1,365; 1,428; 1,470; 1,482; 1,547; 1,596; 1,615; 1,666; 1,729; 1,785; 1,820; 1,862; 1,911; 1,938; 1,995; 2,210; 2,261; 2,380; 2,470; 2,499; 2,548; 2,652; 2,660; 2,730; 2,793; 2,940; 2,964; 3,094; 3,185; 3,230; 3,315; 3,332; 3,458; 3,570; 3,705; 3,724; 3,822; 3,876; 3,990; 4,165; 4,199; 4,420; 4,522; 4,641; 4,655; 4,845; 4,940; 4,998; 5,187; 5,460; 5,586; 6,188; 6,370; 6,460; 6,630; 6,783; 6,916; 7,140; 7,410; 7,644; 7,735; 7,980; 8,330; 8,398; 8,645; 9,044; 9,282; 9,310; 9,555; 9,690; 9,996; 10,374; 10,829; 11,172; 11,305; 12,103; 12,495; 12,597; 12,740; 13,260; 13,566; 13,965; 14,820; 15,470; 15,827; 16,660; 16,796; 17,290; 18,564; 18,620; 19,110; 19,380; 20,748; 20,995; 21,658; 22,610; 23,205; 24,206; 24,990; 25,194; 25,935; 27,132; 27,930; 29,393; 30,940; 31,654; 32,487; 33,915; 34,580; 36,309; 38,220; 41,990; 43,316; 45,220; 46,410; 47,481; 48,412; 49,980; 50,388; 51,870; 54,145; 55,860; 58,786; 60,515; 62,985; 63,308; 64,974; 67,830; 72,618; 79,135; 83,980; 88,179; 92,820; 94,962; 103,740; 108,290; 117,572; 121,030; 125,970; 129,948; 135,660; 145,236; 146,965; 158,270; 162,435; 176,358; 181,545; 189,924; 205,751; 216,580; 237,405; 242,060; 251,940; 293,930; 316,540; 324,870; 352,716; 363,090; 411,502; 440,895; 474,810; 587,860; 617,253; 649,740; 726,180; 823,004; 881,790; 949,620; 1,028,755; 1,234,506; 1,763,580; 2,057,510; 2,469,012; 3,086,265; 4,115,020; 6,172,530 and 12,345,060
out of which 7 prime factors: 2; 3; 5; 7; 13; 17 and 19
12,345,060 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 12,345,059?

» What are all the proper, improper and prime factors (divisors) of the number 12,345,074?


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".