Given the Number 41,538,420 Calculate (Find) All Its Factors (Divisors – the Proper, the Improper and the Prime Factors). Online Calculator

All the factors (divisors) of the number 41,538,420

1. Carry out the prime factorization of the number 41,538,420:

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


41,538,420 = 22 × 36 × 5 × 7 × 11 × 37
41,538,420 is not a prime number but a composite one.


* 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 41,538,420

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
32 = 9
2 × 5 = 10
prime factor = 11
22 × 3 = 12
2 × 7 = 14
3 × 5 = 15
2 × 32 = 18
22 × 5 = 20
3 × 7 = 21
2 × 11 = 22
33 = 27
22 × 7 = 28
2 × 3 × 5 = 30
3 × 11 = 33
5 × 7 = 35
22 × 32 = 36
prime factor = 37
2 × 3 × 7 = 42
22 × 11 = 44
32 × 5 = 45
2 × 33 = 54
5 × 11 = 55
22 × 3 × 5 = 60
32 × 7 = 63
2 × 3 × 11 = 66
2 × 5 × 7 = 70
2 × 37 = 74
7 × 11 = 77
34 = 81
22 × 3 × 7 = 84
2 × 32 × 5 = 90
32 × 11 = 99
3 × 5 × 7 = 105
22 × 33 = 108
2 × 5 × 11 = 110
3 × 37 = 111
2 × 32 × 7 = 126
22 × 3 × 11 = 132
33 × 5 = 135
22 × 5 × 7 = 140
22 × 37 = 148
2 × 7 × 11 = 154
2 × 34 = 162
3 × 5 × 11 = 165
22 × 32 × 5 = 180
5 × 37 = 185
33 × 7 = 189
2 × 32 × 11 = 198
2 × 3 × 5 × 7 = 210
22 × 5 × 11 = 220
2 × 3 × 37 = 222
3 × 7 × 11 = 231
35 = 243
22 × 32 × 7 = 252
7 × 37 = 259
2 × 33 × 5 = 270
33 × 11 = 297
22 × 7 × 11 = 308
32 × 5 × 7 = 315
22 × 34 = 324
2 × 3 × 5 × 11 = 330
32 × 37 = 333
2 × 5 × 37 = 370
2 × 33 × 7 = 378
5 × 7 × 11 = 385
22 × 32 × 11 = 396
34 × 5 = 405
11 × 37 = 407
22 × 3 × 5 × 7 = 420
22 × 3 × 37 = 444
2 × 3 × 7 × 11 = 462
2 × 35 = 486
32 × 5 × 11 = 495
2 × 7 × 37 = 518
22 × 33 × 5 = 540
3 × 5 × 37 = 555
34 × 7 = 567
2 × 33 × 11 = 594
2 × 32 × 5 × 7 = 630
22 × 3 × 5 × 11 = 660
2 × 32 × 37 = 666
32 × 7 × 11 = 693
36 = 729
22 × 5 × 37 = 740
22 × 33 × 7 = 756
2 × 5 × 7 × 11 = 770
3 × 7 × 37 = 777
2 × 34 × 5 = 810
2 × 11 × 37 = 814
34 × 11 = 891
22 × 3 × 7 × 11 = 924
33 × 5 × 7 = 945
22 × 35 = 972
2 × 32 × 5 × 11 = 990
33 × 37 = 999
22 × 7 × 37 = 1,036
2 × 3 × 5 × 37 = 1,110
2 × 34 × 7 = 1,134
3 × 5 × 7 × 11 = 1,155
22 × 33 × 11 = 1,188
35 × 5 = 1,215
3 × 11 × 37 = 1,221
22 × 32 × 5 × 7 = 1,260
5 × 7 × 37 = 1,295
22 × 32 × 37 = 1,332
2 × 32 × 7 × 11 = 1,386
2 × 36 = 1,458
33 × 5 × 11 = 1,485
22 × 5 × 7 × 11 = 1,540
2 × 3 × 7 × 37 = 1,554
22 × 34 × 5 = 1,620
22 × 11 × 37 = 1,628
32 × 5 × 37 = 1,665
35 × 7 = 1,701
2 × 34 × 11 = 1,782
2 × 33 × 5 × 7 = 1,890
22 × 32 × 5 × 11 = 1,980
2 × 33 × 37 = 1,998
5 × 11 × 37 = 2,035
33 × 7 × 11 = 2,079
22 × 3 × 5 × 37 = 2,220
22 × 34 × 7 = 2,268
2 × 3 × 5 × 7 × 11 = 2,310
32 × 7 × 37 = 2,331
2 × 35 × 5 = 2,430
2 × 3 × 11 × 37 = 2,442
2 × 5 × 7 × 37 = 2,590
35 × 11 = 2,673
22 × 32 × 7 × 11 = 2,772
34 × 5 × 7 = 2,835
7 × 11 × 37 = 2,849
22 × 36 = 2,916
2 × 33 × 5 × 11 = 2,970
34 × 37 = 2,997
22 × 3 × 7 × 37 = 3,108
2 × 32 × 5 × 37 = 3,330
2 × 35 × 7 = 3,402
32 × 5 × 7 × 11 = 3,465
22 × 34 × 11 = 3,564
36 × 5 = 3,645
32 × 11 × 37 = 3,663
22 × 33 × 5 × 7 = 3,780
3 × 5 × 7 × 37 = 3,885
22 × 33 × 37 = 3,996
2 × 5 × 11 × 37 = 4,070
2 × 33 × 7 × 11 = 4,158
34 × 5 × 11 = 4,455
22 × 3 × 5 × 7 × 11 = 4,620
2 × 32 × 7 × 37 = 4,662
22 × 35 × 5 = 4,860
22 × 3 × 11 × 37 = 4,884
33 × 5 × 37 = 4,995
36 × 7 = 5,103
22 × 5 × 7 × 37 = 5,180
2 × 35 × 11 = 5,346
2 × 34 × 5 × 7 = 5,670
2 × 7 × 11 × 37 = 5,698
22 × 33 × 5 × 11 = 5,940
2 × 34 × 37 = 5,994
3 × 5 × 11 × 37 = 6,105
34 × 7 × 11 = 6,237
This list continues below...

... This list continues from above
22 × 32 × 5 × 37 = 6,660
22 × 35 × 7 = 6,804
2 × 32 × 5 × 7 × 11 = 6,930
33 × 7 × 37 = 6,993
2 × 36 × 5 = 7,290
2 × 32 × 11 × 37 = 7,326
2 × 3 × 5 × 7 × 37 = 7,770
36 × 11 = 8,019
22 × 5 × 11 × 37 = 8,140
22 × 33 × 7 × 11 = 8,316
35 × 5 × 7 = 8,505
3 × 7 × 11 × 37 = 8,547
2 × 34 × 5 × 11 = 8,910
35 × 37 = 8,991
22 × 32 × 7 × 37 = 9,324
2 × 33 × 5 × 37 = 9,990
2 × 36 × 7 = 10,206
33 × 5 × 7 × 11 = 10,395
22 × 35 × 11 = 10,692
33 × 11 × 37 = 10,989
22 × 34 × 5 × 7 = 11,340
22 × 7 × 11 × 37 = 11,396
32 × 5 × 7 × 37 = 11,655
22 × 34 × 37 = 11,988
2 × 3 × 5 × 11 × 37 = 12,210
2 × 34 × 7 × 11 = 12,474
35 × 5 × 11 = 13,365
22 × 32 × 5 × 7 × 11 = 13,860
2 × 33 × 7 × 37 = 13,986
5 × 7 × 11 × 37 = 14,245
22 × 36 × 5 = 14,580
22 × 32 × 11 × 37 = 14,652
34 × 5 × 37 = 14,985
22 × 3 × 5 × 7 × 37 = 15,540
2 × 36 × 11 = 16,038
2 × 35 × 5 × 7 = 17,010
2 × 3 × 7 × 11 × 37 = 17,094
22 × 34 × 5 × 11 = 17,820
2 × 35 × 37 = 17,982
32 × 5 × 11 × 37 = 18,315
35 × 7 × 11 = 18,711
22 × 33 × 5 × 37 = 19,980
22 × 36 × 7 = 20,412
2 × 33 × 5 × 7 × 11 = 20,790
34 × 7 × 37 = 20,979
2 × 33 × 11 × 37 = 21,978
2 × 32 × 5 × 7 × 37 = 23,310
22 × 3 × 5 × 11 × 37 = 24,420
22 × 34 × 7 × 11 = 24,948
36 × 5 × 7 = 25,515
32 × 7 × 11 × 37 = 25,641
2 × 35 × 5 × 11 = 26,730
36 × 37 = 26,973
22 × 33 × 7 × 37 = 27,972
2 × 5 × 7 × 11 × 37 = 28,490
2 × 34 × 5 × 37 = 29,970
34 × 5 × 7 × 11 = 31,185
22 × 36 × 11 = 32,076
34 × 11 × 37 = 32,967
22 × 35 × 5 × 7 = 34,020
22 × 3 × 7 × 11 × 37 = 34,188
33 × 5 × 7 × 37 = 34,965
22 × 35 × 37 = 35,964
2 × 32 × 5 × 11 × 37 = 36,630
2 × 35 × 7 × 11 = 37,422
36 × 5 × 11 = 40,095
22 × 33 × 5 × 7 × 11 = 41,580
2 × 34 × 7 × 37 = 41,958
3 × 5 × 7 × 11 × 37 = 42,735
22 × 33 × 11 × 37 = 43,956
35 × 5 × 37 = 44,955
22 × 32 × 5 × 7 × 37 = 46,620
2 × 36 × 5 × 7 = 51,030
2 × 32 × 7 × 11 × 37 = 51,282
22 × 35 × 5 × 11 = 53,460
2 × 36 × 37 = 53,946
33 × 5 × 11 × 37 = 54,945
36 × 7 × 11 = 56,133
22 × 5 × 7 × 11 × 37 = 56,980
22 × 34 × 5 × 37 = 59,940
2 × 34 × 5 × 7 × 11 = 62,370
35 × 7 × 37 = 62,937
2 × 34 × 11 × 37 = 65,934
2 × 33 × 5 × 7 × 37 = 69,930
22 × 32 × 5 × 11 × 37 = 73,260
22 × 35 × 7 × 11 = 74,844
33 × 7 × 11 × 37 = 76,923
2 × 36 × 5 × 11 = 80,190
22 × 34 × 7 × 37 = 83,916
2 × 3 × 5 × 7 × 11 × 37 = 85,470
2 × 35 × 5 × 37 = 89,910
35 × 5 × 7 × 11 = 93,555
35 × 11 × 37 = 98,901
22 × 36 × 5 × 7 = 102,060
22 × 32 × 7 × 11 × 37 = 102,564
34 × 5 × 7 × 37 = 104,895
22 × 36 × 37 = 107,892
2 × 33 × 5 × 11 × 37 = 109,890
2 × 36 × 7 × 11 = 112,266
22 × 34 × 5 × 7 × 11 = 124,740
2 × 35 × 7 × 37 = 125,874
32 × 5 × 7 × 11 × 37 = 128,205
22 × 34 × 11 × 37 = 131,868
36 × 5 × 37 = 134,865
22 × 33 × 5 × 7 × 37 = 139,860
2 × 33 × 7 × 11 × 37 = 153,846
22 × 36 × 5 × 11 = 160,380
34 × 5 × 11 × 37 = 164,835
22 × 3 × 5 × 7 × 11 × 37 = 170,940
22 × 35 × 5 × 37 = 179,820
2 × 35 × 5 × 7 × 11 = 187,110
36 × 7 × 37 = 188,811
2 × 35 × 11 × 37 = 197,802
2 × 34 × 5 × 7 × 37 = 209,790
22 × 33 × 5 × 11 × 37 = 219,780
22 × 36 × 7 × 11 = 224,532
34 × 7 × 11 × 37 = 230,769
22 × 35 × 7 × 37 = 251,748
2 × 32 × 5 × 7 × 11 × 37 = 256,410
2 × 36 × 5 × 37 = 269,730
36 × 5 × 7 × 11 = 280,665
36 × 11 × 37 = 296,703
22 × 33 × 7 × 11 × 37 = 307,692
35 × 5 × 7 × 37 = 314,685
2 × 34 × 5 × 11 × 37 = 329,670
22 × 35 × 5 × 7 × 11 = 374,220
2 × 36 × 7 × 37 = 377,622
33 × 5 × 7 × 11 × 37 = 384,615
22 × 35 × 11 × 37 = 395,604
22 × 34 × 5 × 7 × 37 = 419,580
2 × 34 × 7 × 11 × 37 = 461,538
35 × 5 × 11 × 37 = 494,505
22 × 32 × 5 × 7 × 11 × 37 = 512,820
22 × 36 × 5 × 37 = 539,460
2 × 36 × 5 × 7 × 11 = 561,330
2 × 36 × 11 × 37 = 593,406
2 × 35 × 5 × 7 × 37 = 629,370
22 × 34 × 5 × 11 × 37 = 659,340
35 × 7 × 11 × 37 = 692,307
22 × 36 × 7 × 37 = 755,244
2 × 33 × 5 × 7 × 11 × 37 = 769,230
22 × 34 × 7 × 11 × 37 = 923,076
36 × 5 × 7 × 37 = 944,055
2 × 35 × 5 × 11 × 37 = 989,010
22 × 36 × 5 × 7 × 11 = 1,122,660
34 × 5 × 7 × 11 × 37 = 1,153,845
22 × 36 × 11 × 37 = 1,186,812
22 × 35 × 5 × 7 × 37 = 1,258,740
2 × 35 × 7 × 11 × 37 = 1,384,614
36 × 5 × 11 × 37 = 1,483,515
22 × 33 × 5 × 7 × 11 × 37 = 1,538,460
2 × 36 × 5 × 7 × 37 = 1,888,110
22 × 35 × 5 × 11 × 37 = 1,978,020
36 × 7 × 11 × 37 = 2,076,921
2 × 34 × 5 × 7 × 11 × 37 = 2,307,690
22 × 35 × 7 × 11 × 37 = 2,769,228
2 × 36 × 5 × 11 × 37 = 2,967,030
35 × 5 × 7 × 11 × 37 = 3,461,535
22 × 36 × 5 × 7 × 37 = 3,776,220
2 × 36 × 7 × 11 × 37 = 4,153,842
22 × 34 × 5 × 7 × 11 × 37 = 4,615,380
22 × 36 × 5 × 11 × 37 = 5,934,060
2 × 35 × 5 × 7 × 11 × 37 = 6,923,070
22 × 36 × 7 × 11 × 37 = 8,307,684
36 × 5 × 7 × 11 × 37 = 10,384,605
22 × 35 × 5 × 7 × 11 × 37 = 13,846,140
2 × 36 × 5 × 7 × 11 × 37 = 20,769,210
22 × 36 × 5 × 7 × 11 × 37 = 41,538,420

The final answer:
(scroll down)

41,538,420 has 336 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 9; 10; 11; 12; 14; 15; 18; 20; 21; 22; 27; 28; 30; 33; 35; 36; 37; 42; 44; 45; 54; 55; 60; 63; 66; 70; 74; 77; 81; 84; 90; 99; 105; 108; 110; 111; 126; 132; 135; 140; 148; 154; 162; 165; 180; 185; 189; 198; 210; 220; 222; 231; 243; 252; 259; 270; 297; 308; 315; 324; 330; 333; 370; 378; 385; 396; 405; 407; 420; 444; 462; 486; 495; 518; 540; 555; 567; 594; 630; 660; 666; 693; 729; 740; 756; 770; 777; 810; 814; 891; 924; 945; 972; 990; 999; 1,036; 1,110; 1,134; 1,155; 1,188; 1,215; 1,221; 1,260; 1,295; 1,332; 1,386; 1,458; 1,485; 1,540; 1,554; 1,620; 1,628; 1,665; 1,701; 1,782; 1,890; 1,980; 1,998; 2,035; 2,079; 2,220; 2,268; 2,310; 2,331; 2,430; 2,442; 2,590; 2,673; 2,772; 2,835; 2,849; 2,916; 2,970; 2,997; 3,108; 3,330; 3,402; 3,465; 3,564; 3,645; 3,663; 3,780; 3,885; 3,996; 4,070; 4,158; 4,455; 4,620; 4,662; 4,860; 4,884; 4,995; 5,103; 5,180; 5,346; 5,670; 5,698; 5,940; 5,994; 6,105; 6,237; 6,660; 6,804; 6,930; 6,993; 7,290; 7,326; 7,770; 8,019; 8,140; 8,316; 8,505; 8,547; 8,910; 8,991; 9,324; 9,990; 10,206; 10,395; 10,692; 10,989; 11,340; 11,396; 11,655; 11,988; 12,210; 12,474; 13,365; 13,860; 13,986; 14,245; 14,580; 14,652; 14,985; 15,540; 16,038; 17,010; 17,094; 17,820; 17,982; 18,315; 18,711; 19,980; 20,412; 20,790; 20,979; 21,978; 23,310; 24,420; 24,948; 25,515; 25,641; 26,730; 26,973; 27,972; 28,490; 29,970; 31,185; 32,076; 32,967; 34,020; 34,188; 34,965; 35,964; 36,630; 37,422; 40,095; 41,580; 41,958; 42,735; 43,956; 44,955; 46,620; 51,030; 51,282; 53,460; 53,946; 54,945; 56,133; 56,980; 59,940; 62,370; 62,937; 65,934; 69,930; 73,260; 74,844; 76,923; 80,190; 83,916; 85,470; 89,910; 93,555; 98,901; 102,060; 102,564; 104,895; 107,892; 109,890; 112,266; 124,740; 125,874; 128,205; 131,868; 134,865; 139,860; 153,846; 160,380; 164,835; 170,940; 179,820; 187,110; 188,811; 197,802; 209,790; 219,780; 224,532; 230,769; 251,748; 256,410; 269,730; 280,665; 296,703; 307,692; 314,685; 329,670; 374,220; 377,622; 384,615; 395,604; 419,580; 461,538; 494,505; 512,820; 539,460; 561,330; 593,406; 629,370; 659,340; 692,307; 755,244; 769,230; 923,076; 944,055; 989,010; 1,122,660; 1,153,845; 1,186,812; 1,258,740; 1,384,614; 1,483,515; 1,538,460; 1,888,110; 1,978,020; 2,076,921; 2,307,690; 2,769,228; 2,967,030; 3,461,535; 3,776,220; 4,153,842; 4,615,380; 5,934,060; 6,923,070; 8,307,684; 10,384,605; 13,846,140; 20,769,210 and 41,538,420
out of which 6 prime factors: 2; 3; 5; 7; 11 and 37
41,538,420 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.


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".