Given the Number 49,827,960, Calculate (Find) All the Factors (All the Divisors) of the Number 49,827,960 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 49,827,960

1. Carry out the prime factorization of the number 49,827,960:

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

49,827,960 = 23 × 34 × 5 × 7 × 133
49,827,960 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 49,827,960

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
32 = 9
2 × 5 = 10
22 × 3 = 12
prime factor = 13
2 × 7 = 14
3 × 5 = 15
2 × 32 = 18
22 × 5 = 20
3 × 7 = 21
23 × 3 = 24
2 × 13 = 26
33 = 27
22 × 7 = 28
2 × 3 × 5 = 30
5 × 7 = 35
22 × 32 = 36
3 × 13 = 39
23 × 5 = 40
2 × 3 × 7 = 42
32 × 5 = 45
22 × 13 = 52
2 × 33 = 54
23 × 7 = 56
22 × 3 × 5 = 60
32 × 7 = 63
5 × 13 = 65
2 × 5 × 7 = 70
23 × 32 = 72
2 × 3 × 13 = 78
34 = 81
22 × 3 × 7 = 84
2 × 32 × 5 = 90
7 × 13 = 91
23 × 13 = 104
3 × 5 × 7 = 105
22 × 33 = 108
32 × 13 = 117
23 × 3 × 5 = 120
2 × 32 × 7 = 126
2 × 5 × 13 = 130
33 × 5 = 135
22 × 5 × 7 = 140
22 × 3 × 13 = 156
2 × 34 = 162
23 × 3 × 7 = 168
132 = 169
22 × 32 × 5 = 180
2 × 7 × 13 = 182
33 × 7 = 189
3 × 5 × 13 = 195
2 × 3 × 5 × 7 = 210
23 × 33 = 216
2 × 32 × 13 = 234
22 × 32 × 7 = 252
22 × 5 × 13 = 260
2 × 33 × 5 = 270
3 × 7 × 13 = 273
23 × 5 × 7 = 280
23 × 3 × 13 = 312
32 × 5 × 7 = 315
22 × 34 = 324
2 × 132 = 338
33 × 13 = 351
23 × 32 × 5 = 360
22 × 7 × 13 = 364
2 × 33 × 7 = 378
2 × 3 × 5 × 13 = 390
34 × 5 = 405
22 × 3 × 5 × 7 = 420
5 × 7 × 13 = 455
22 × 32 × 13 = 468
23 × 32 × 7 = 504
3 × 132 = 507
23 × 5 × 13 = 520
22 × 33 × 5 = 540
2 × 3 × 7 × 13 = 546
34 × 7 = 567
32 × 5 × 13 = 585
2 × 32 × 5 × 7 = 630
23 × 34 = 648
22 × 132 = 676
2 × 33 × 13 = 702
23 × 7 × 13 = 728
22 × 33 × 7 = 756
22 × 3 × 5 × 13 = 780
2 × 34 × 5 = 810
32 × 7 × 13 = 819
23 × 3 × 5 × 7 = 840
5 × 132 = 845
2 × 5 × 7 × 13 = 910
23 × 32 × 13 = 936
33 × 5 × 7 = 945
2 × 3 × 132 = 1,014
34 × 13 = 1,053
23 × 33 × 5 = 1,080
22 × 3 × 7 × 13 = 1,092
2 × 34 × 7 = 1,134
2 × 32 × 5 × 13 = 1,170
7 × 132 = 1,183
22 × 32 × 5 × 7 = 1,260
23 × 132 = 1,352
3 × 5 × 7 × 13 = 1,365
22 × 33 × 13 = 1,404
23 × 33 × 7 = 1,512
32 × 132 = 1,521
23 × 3 × 5 × 13 = 1,560
22 × 34 × 5 = 1,620
2 × 32 × 7 × 13 = 1,638
2 × 5 × 132 = 1,690
33 × 5 × 13 = 1,755
22 × 5 × 7 × 13 = 1,820
2 × 33 × 5 × 7 = 1,890
22 × 3 × 132 = 2,028
2 × 34 × 13 = 2,106
23 × 3 × 7 × 13 = 2,184
133 = 2,197
22 × 34 × 7 = 2,268
22 × 32 × 5 × 13 = 2,340
2 × 7 × 132 = 2,366
33 × 7 × 13 = 2,457
23 × 32 × 5 × 7 = 2,520
3 × 5 × 132 = 2,535
2 × 3 × 5 × 7 × 13 = 2,730
23 × 33 × 13 = 2,808
34 × 5 × 7 = 2,835
2 × 32 × 132 = 3,042
23 × 34 × 5 = 3,240
22 × 32 × 7 × 13 = 3,276
22 × 5 × 132 = 3,380
2 × 33 × 5 × 13 = 3,510
3 × 7 × 132 = 3,549
23 × 5 × 7 × 13 = 3,640
22 × 33 × 5 × 7 = 3,780
23 × 3 × 132 = 4,056
32 × 5 × 7 × 13 = 4,095
22 × 34 × 13 = 4,212
2 × 133 = 4,394
23 × 34 × 7 = 4,536
33 × 132 = 4,563
23 × 32 × 5 × 13 = 4,680
22 × 7 × 132 = 4,732
2 × 33 × 7 × 13 = 4,914
2 × 3 × 5 × 132 = 5,070
34 × 5 × 13 = 5,265
22 × 3 × 5 × 7 × 13 = 5,460
2 × 34 × 5 × 7 = 5,670
5 × 7 × 132 = 5,915
22 × 32 × 132 = 6,084
23 × 32 × 7 × 13 = 6,552
3 × 133 = 6,591
23 × 5 × 132 = 6,760
22 × 33 × 5 × 13 = 7,020
This list continues below...

... This list continues from above
2 × 3 × 7 × 132 = 7,098
34 × 7 × 13 = 7,371
23 × 33 × 5 × 7 = 7,560
32 × 5 × 132 = 7,605
2 × 32 × 5 × 7 × 13 = 8,190
23 × 34 × 13 = 8,424
22 × 133 = 8,788
2 × 33 × 132 = 9,126
23 × 7 × 132 = 9,464
22 × 33 × 7 × 13 = 9,828
22 × 3 × 5 × 132 = 10,140
2 × 34 × 5 × 13 = 10,530
32 × 7 × 132 = 10,647
23 × 3 × 5 × 7 × 13 = 10,920
5 × 133 = 10,985
22 × 34 × 5 × 7 = 11,340
2 × 5 × 7 × 132 = 11,830
23 × 32 × 132 = 12,168
33 × 5 × 7 × 13 = 12,285
2 × 3 × 133 = 13,182
34 × 132 = 13,689
23 × 33 × 5 × 13 = 14,040
22 × 3 × 7 × 132 = 14,196
2 × 34 × 7 × 13 = 14,742
2 × 32 × 5 × 132 = 15,210
7 × 133 = 15,379
22 × 32 × 5 × 7 × 13 = 16,380
23 × 133 = 17,576
3 × 5 × 7 × 132 = 17,745
22 × 33 × 132 = 18,252
23 × 33 × 7 × 13 = 19,656
32 × 133 = 19,773
23 × 3 × 5 × 132 = 20,280
22 × 34 × 5 × 13 = 21,060
2 × 32 × 7 × 132 = 21,294
2 × 5 × 133 = 21,970
23 × 34 × 5 × 7 = 22,680
33 × 5 × 132 = 22,815
22 × 5 × 7 × 132 = 23,660
2 × 33 × 5 × 7 × 13 = 24,570
22 × 3 × 133 = 26,364
2 × 34 × 132 = 27,378
23 × 3 × 7 × 132 = 28,392
22 × 34 × 7 × 13 = 29,484
22 × 32 × 5 × 132 = 30,420
2 × 7 × 133 = 30,758
33 × 7 × 132 = 31,941
23 × 32 × 5 × 7 × 13 = 32,760
3 × 5 × 133 = 32,955
2 × 3 × 5 × 7 × 132 = 35,490
23 × 33 × 132 = 36,504
34 × 5 × 7 × 13 = 36,855
2 × 32 × 133 = 39,546
23 × 34 × 5 × 13 = 42,120
22 × 32 × 7 × 132 = 42,588
22 × 5 × 133 = 43,940
2 × 33 × 5 × 132 = 45,630
3 × 7 × 133 = 46,137
23 × 5 × 7 × 132 = 47,320
22 × 33 × 5 × 7 × 13 = 49,140
23 × 3 × 133 = 52,728
32 × 5 × 7 × 132 = 53,235
22 × 34 × 132 = 54,756
23 × 34 × 7 × 13 = 58,968
33 × 133 = 59,319
23 × 32 × 5 × 132 = 60,840
22 × 7 × 133 = 61,516
2 × 33 × 7 × 132 = 63,882
2 × 3 × 5 × 133 = 65,910
34 × 5 × 132 = 68,445
22 × 3 × 5 × 7 × 132 = 70,980
2 × 34 × 5 × 7 × 13 = 73,710
5 × 7 × 133 = 76,895
22 × 32 × 133 = 79,092
23 × 32 × 7 × 132 = 85,176
23 × 5 × 133 = 87,880
22 × 33 × 5 × 132 = 91,260
2 × 3 × 7 × 133 = 92,274
34 × 7 × 132 = 95,823
23 × 33 × 5 × 7 × 13 = 98,280
32 × 5 × 133 = 98,865
2 × 32 × 5 × 7 × 132 = 106,470
23 × 34 × 132 = 109,512
2 × 33 × 133 = 118,638
23 × 7 × 133 = 123,032
22 × 33 × 7 × 132 = 127,764
22 × 3 × 5 × 133 = 131,820
2 × 34 × 5 × 132 = 136,890
32 × 7 × 133 = 138,411
23 × 3 × 5 × 7 × 132 = 141,960
22 × 34 × 5 × 7 × 13 = 147,420
2 × 5 × 7 × 133 = 153,790
23 × 32 × 133 = 158,184
33 × 5 × 7 × 132 = 159,705
34 × 133 = 177,957
23 × 33 × 5 × 132 = 182,520
22 × 3 × 7 × 133 = 184,548
2 × 34 × 7 × 132 = 191,646
2 × 32 × 5 × 133 = 197,730
22 × 32 × 5 × 7 × 132 = 212,940
3 × 5 × 7 × 133 = 230,685
22 × 33 × 133 = 237,276
23 × 33 × 7 × 132 = 255,528
23 × 3 × 5 × 133 = 263,640
22 × 34 × 5 × 132 = 273,780
2 × 32 × 7 × 133 = 276,822
23 × 34 × 5 × 7 × 13 = 294,840
33 × 5 × 133 = 296,595
22 × 5 × 7 × 133 = 307,580
2 × 33 × 5 × 7 × 132 = 319,410
2 × 34 × 133 = 355,914
23 × 3 × 7 × 133 = 369,096
22 × 34 × 7 × 132 = 383,292
22 × 32 × 5 × 133 = 395,460
33 × 7 × 133 = 415,233
23 × 32 × 5 × 7 × 132 = 425,880
2 × 3 × 5 × 7 × 133 = 461,370
23 × 33 × 133 = 474,552
34 × 5 × 7 × 132 = 479,115
23 × 34 × 5 × 132 = 547,560
22 × 32 × 7 × 133 = 553,644
2 × 33 × 5 × 133 = 593,190
23 × 5 × 7 × 133 = 615,160
22 × 33 × 5 × 7 × 132 = 638,820
32 × 5 × 7 × 133 = 692,055
22 × 34 × 133 = 711,828
23 × 34 × 7 × 132 = 766,584
23 × 32 × 5 × 133 = 790,920
2 × 33 × 7 × 133 = 830,466
34 × 5 × 133 = 889,785
22 × 3 × 5 × 7 × 133 = 922,740
2 × 34 × 5 × 7 × 132 = 958,230
23 × 32 × 7 × 133 = 1,107,288
22 × 33 × 5 × 133 = 1,186,380
34 × 7 × 133 = 1,245,699
23 × 33 × 5 × 7 × 132 = 1,277,640
2 × 32 × 5 × 7 × 133 = 1,384,110
23 × 34 × 133 = 1,423,656
22 × 33 × 7 × 133 = 1,660,932
2 × 34 × 5 × 133 = 1,779,570
23 × 3 × 5 × 7 × 133 = 1,845,480
22 × 34 × 5 × 7 × 132 = 1,916,460
33 × 5 × 7 × 133 = 2,076,165
23 × 33 × 5 × 133 = 2,372,760
2 × 34 × 7 × 133 = 2,491,398
22 × 32 × 5 × 7 × 133 = 2,768,220
23 × 33 × 7 × 133 = 3,321,864
22 × 34 × 5 × 133 = 3,559,140
23 × 34 × 5 × 7 × 132 = 3,832,920
2 × 33 × 5 × 7 × 133 = 4,152,330
22 × 34 × 7 × 133 = 4,982,796
23 × 32 × 5 × 7 × 133 = 5,536,440
34 × 5 × 7 × 133 = 6,228,495
23 × 34 × 5 × 133 = 7,118,280
22 × 33 × 5 × 7 × 133 = 8,304,660
23 × 34 × 7 × 133 = 9,965,592
2 × 34 × 5 × 7 × 133 = 12,456,990
23 × 33 × 5 × 7 × 133 = 16,609,320
22 × 34 × 5 × 7 × 133 = 24,913,980
23 × 34 × 5 × 7 × 133 = 49,827,960

The final answer:
(scroll down)

49,827,960 has 320 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 12; 13; 14; 15; 18; 20; 21; 24; 26; 27; 28; 30; 35; 36; 39; 40; 42; 45; 52; 54; 56; 60; 63; 65; 70; 72; 78; 81; 84; 90; 91; 104; 105; 108; 117; 120; 126; 130; 135; 140; 156; 162; 168; 169; 180; 182; 189; 195; 210; 216; 234; 252; 260; 270; 273; 280; 312; 315; 324; 338; 351; 360; 364; 378; 390; 405; 420; 455; 468; 504; 507; 520; 540; 546; 567; 585; 630; 648; 676; 702; 728; 756; 780; 810; 819; 840; 845; 910; 936; 945; 1,014; 1,053; 1,080; 1,092; 1,134; 1,170; 1,183; 1,260; 1,352; 1,365; 1,404; 1,512; 1,521; 1,560; 1,620; 1,638; 1,690; 1,755; 1,820; 1,890; 2,028; 2,106; 2,184; 2,197; 2,268; 2,340; 2,366; 2,457; 2,520; 2,535; 2,730; 2,808; 2,835; 3,042; 3,240; 3,276; 3,380; 3,510; 3,549; 3,640; 3,780; 4,056; 4,095; 4,212; 4,394; 4,536; 4,563; 4,680; 4,732; 4,914; 5,070; 5,265; 5,460; 5,670; 5,915; 6,084; 6,552; 6,591; 6,760; 7,020; 7,098; 7,371; 7,560; 7,605; 8,190; 8,424; 8,788; 9,126; 9,464; 9,828; 10,140; 10,530; 10,647; 10,920; 10,985; 11,340; 11,830; 12,168; 12,285; 13,182; 13,689; 14,040; 14,196; 14,742; 15,210; 15,379; 16,380; 17,576; 17,745; 18,252; 19,656; 19,773; 20,280; 21,060; 21,294; 21,970; 22,680; 22,815; 23,660; 24,570; 26,364; 27,378; 28,392; 29,484; 30,420; 30,758; 31,941; 32,760; 32,955; 35,490; 36,504; 36,855; 39,546; 42,120; 42,588; 43,940; 45,630; 46,137; 47,320; 49,140; 52,728; 53,235; 54,756; 58,968; 59,319; 60,840; 61,516; 63,882; 65,910; 68,445; 70,980; 73,710; 76,895; 79,092; 85,176; 87,880; 91,260; 92,274; 95,823; 98,280; 98,865; 106,470; 109,512; 118,638; 123,032; 127,764; 131,820; 136,890; 138,411; 141,960; 147,420; 153,790; 158,184; 159,705; 177,957; 182,520; 184,548; 191,646; 197,730; 212,940; 230,685; 237,276; 255,528; 263,640; 273,780; 276,822; 294,840; 296,595; 307,580; 319,410; 355,914; 369,096; 383,292; 395,460; 415,233; 425,880; 461,370; 474,552; 479,115; 547,560; 553,644; 593,190; 615,160; 638,820; 692,055; 711,828; 766,584; 790,920; 830,466; 889,785; 922,740; 958,230; 1,107,288; 1,186,380; 1,245,699; 1,277,640; 1,384,110; 1,423,656; 1,660,932; 1,779,570; 1,845,480; 1,916,460; 2,076,165; 2,372,760; 2,491,398; 2,768,220; 3,321,864; 3,559,140; 3,832,920; 4,152,330; 4,982,796; 5,536,440; 6,228,495; 7,118,280; 8,304,660; 9,965,592; 12,456,990; 16,609,320; 24,913,980 and 49,827,960
out of which 5 prime factors: 2; 3; 5; 7 and 13
49,827,960 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 49,827,954?

» What are all the proper, improper and prime factors (divisors) of the number 49,827,975?


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".