Given the Number 33,218,640, Calculate (Find) All the Factors (All the Divisors) of the Number 33,218,640 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 33,218,640

1. Carry out the prime factorization of the number 33,218,640:

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

33,218,640 = 24 × 33 × 5 × 7 × 133
33,218,640 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 33,218,640

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
24 = 16
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
24 × 3 = 48
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
24 × 5 = 80
22 × 3 × 7 = 84
2 × 32 × 5 = 90
7 × 13 = 91
23 × 13 = 104
3 × 5 × 7 = 105
22 × 33 = 108
24 × 7 = 112
32 × 13 = 117
23 × 3 × 5 = 120
2 × 32 × 7 = 126
2 × 5 × 13 = 130
33 × 5 = 135
22 × 5 × 7 = 140
24 × 32 = 144
22 × 3 × 13 = 156
23 × 3 × 7 = 168
132 = 169
22 × 32 × 5 = 180
2 × 7 × 13 = 182
33 × 7 = 189
3 × 5 × 13 = 195
24 × 13 = 208
2 × 3 × 5 × 7 = 210
23 × 33 = 216
2 × 32 × 13 = 234
24 × 3 × 5 = 240
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
24 × 3 × 7 = 336
2 × 132 = 338
33 × 13 = 351
23 × 32 × 5 = 360
22 × 7 × 13 = 364
2 × 33 × 7 = 378
2 × 3 × 5 × 13 = 390
22 × 3 × 5 × 7 = 420
24 × 33 = 432
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
24 × 5 × 7 = 560
32 × 5 × 13 = 585
24 × 3 × 13 = 624
2 × 32 × 5 × 7 = 630
22 × 132 = 676
2 × 33 × 13 = 702
24 × 32 × 5 = 720
23 × 7 × 13 = 728
22 × 33 × 7 = 756
22 × 3 × 5 × 13 = 780
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
24 × 32 × 7 = 1,008
2 × 3 × 132 = 1,014
24 × 5 × 13 = 1,040
23 × 33 × 5 = 1,080
22 × 3 × 7 × 13 = 1,092
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
24 × 7 × 13 = 1,456
23 × 33 × 7 = 1,512
32 × 132 = 1,521
23 × 3 × 5 × 13 = 1,560
2 × 32 × 7 × 13 = 1,638
24 × 3 × 5 × 7 = 1,680
2 × 5 × 132 = 1,690
33 × 5 × 13 = 1,755
22 × 5 × 7 × 13 = 1,820
24 × 32 × 13 = 1,872
2 × 33 × 5 × 7 = 1,890
22 × 3 × 132 = 2,028
24 × 33 × 5 = 2,160
23 × 3 × 7 × 13 = 2,184
133 = 2,197
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
24 × 132 = 2,704
2 × 3 × 5 × 7 × 13 = 2,730
23 × 33 × 13 = 2,808
24 × 33 × 7 = 3,024
2 × 32 × 132 = 3,042
24 × 3 × 5 × 13 = 3,120
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
24 × 3 × 7 × 13 = 4,368
2 × 133 = 4,394
33 × 132 = 4,563
23 × 32 × 5 × 13 = 4,680
22 × 7 × 132 = 4,732
2 × 33 × 7 × 13 = 4,914
24 × 32 × 5 × 7 = 5,040
2 × 3 × 5 × 132 = 5,070
22 × 3 × 5 × 7 × 13 = 5,460
24 × 33 × 13 = 5,616
This list continues below...

... This list continues from above
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
2 × 3 × 7 × 132 = 7,098
24 × 5 × 7 × 13 = 7,280
23 × 33 × 5 × 7 = 7,560
32 × 5 × 132 = 7,605
24 × 3 × 132 = 8,112
2 × 32 × 5 × 7 × 13 = 8,190
22 × 133 = 8,788
2 × 33 × 132 = 9,126
24 × 32 × 5 × 13 = 9,360
23 × 7 × 132 = 9,464
22 × 33 × 7 × 13 = 9,828
22 × 3 × 5 × 132 = 10,140
32 × 7 × 132 = 10,647
23 × 3 × 5 × 7 × 13 = 10,920
5 × 133 = 10,985
2 × 5 × 7 × 132 = 11,830
23 × 32 × 132 = 12,168
33 × 5 × 7 × 13 = 12,285
24 × 32 × 7 × 13 = 13,104
2 × 3 × 133 = 13,182
24 × 5 × 132 = 13,520
23 × 33 × 5 × 13 = 14,040
22 × 3 × 7 × 132 = 14,196
24 × 33 × 5 × 7 = 15,120
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
24 × 7 × 132 = 18,928
23 × 33 × 7 × 13 = 19,656
32 × 133 = 19,773
23 × 3 × 5 × 132 = 20,280
2 × 32 × 7 × 132 = 21,294
24 × 3 × 5 × 7 × 13 = 21,840
2 × 5 × 133 = 21,970
33 × 5 × 132 = 22,815
22 × 5 × 7 × 132 = 23,660
24 × 32 × 132 = 24,336
2 × 33 × 5 × 7 × 13 = 24,570
22 × 3 × 133 = 26,364
24 × 33 × 5 × 13 = 28,080
23 × 3 × 7 × 132 = 28,392
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
24 × 133 = 35,152
2 × 3 × 5 × 7 × 132 = 35,490
23 × 33 × 132 = 36,504
24 × 33 × 7 × 13 = 39,312
2 × 32 × 133 = 39,546
24 × 3 × 5 × 132 = 40,560
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
24 × 3 × 7 × 132 = 56,784
33 × 133 = 59,319
23 × 32 × 5 × 132 = 60,840
22 × 7 × 133 = 61,516
2 × 33 × 7 × 132 = 63,882
24 × 32 × 5 × 7 × 13 = 65,520
2 × 3 × 5 × 133 = 65,910
22 × 3 × 5 × 7 × 132 = 70,980
24 × 33 × 132 = 73,008
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
24 × 5 × 7 × 132 = 94,640
23 × 33 × 5 × 7 × 13 = 98,280
32 × 5 × 133 = 98,865
24 × 3 × 133 = 105,456
2 × 32 × 5 × 7 × 132 = 106,470
2 × 33 × 133 = 118,638
24 × 32 × 5 × 132 = 121,680
23 × 7 × 133 = 123,032
22 × 33 × 7 × 132 = 127,764
22 × 3 × 5 × 133 = 131,820
32 × 7 × 133 = 138,411
23 × 3 × 5 × 7 × 132 = 141,960
2 × 5 × 7 × 133 = 153,790
23 × 32 × 133 = 158,184
33 × 5 × 7 × 132 = 159,705
24 × 32 × 7 × 132 = 170,352
24 × 5 × 133 = 175,760
23 × 33 × 5 × 132 = 182,520
22 × 3 × 7 × 133 = 184,548
24 × 33 × 5 × 7 × 13 = 196,560
2 × 32 × 5 × 133 = 197,730
22 × 32 × 5 × 7 × 132 = 212,940
3 × 5 × 7 × 133 = 230,685
22 × 33 × 133 = 237,276
24 × 7 × 133 = 246,064
23 × 33 × 7 × 132 = 255,528
23 × 3 × 5 × 133 = 263,640
2 × 32 × 7 × 133 = 276,822
24 × 3 × 5 × 7 × 132 = 283,920
33 × 5 × 133 = 296,595
22 × 5 × 7 × 133 = 307,580
24 × 32 × 133 = 316,368
2 × 33 × 5 × 7 × 132 = 319,410
24 × 33 × 5 × 132 = 365,040
23 × 3 × 7 × 133 = 369,096
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
24 × 33 × 7 × 132 = 511,056
24 × 3 × 5 × 133 = 527,280
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
24 × 3 × 7 × 133 = 738,192
23 × 32 × 5 × 133 = 790,920
2 × 33 × 7 × 133 = 830,466
24 × 32 × 5 × 7 × 132 = 851,760
22 × 3 × 5 × 7 × 133 = 922,740
24 × 33 × 133 = 949,104
23 × 32 × 7 × 133 = 1,107,288
22 × 33 × 5 × 133 = 1,186,380
24 × 5 × 7 × 133 = 1,230,320
23 × 33 × 5 × 7 × 132 = 1,277,640
2 × 32 × 5 × 7 × 133 = 1,384,110
24 × 32 × 5 × 133 = 1,581,840
22 × 33 × 7 × 133 = 1,660,932
23 × 3 × 5 × 7 × 133 = 1,845,480
33 × 5 × 7 × 133 = 2,076,165
24 × 32 × 7 × 133 = 2,214,576
23 × 33 × 5 × 133 = 2,372,760
24 × 33 × 5 × 7 × 132 = 2,555,280
22 × 32 × 5 × 7 × 133 = 2,768,220
23 × 33 × 7 × 133 = 3,321,864
24 × 3 × 5 × 7 × 133 = 3,690,960
2 × 33 × 5 × 7 × 133 = 4,152,330
24 × 33 × 5 × 133 = 4,745,520
23 × 32 × 5 × 7 × 133 = 5,536,440
24 × 33 × 7 × 133 = 6,643,728
22 × 33 × 5 × 7 × 133 = 8,304,660
24 × 32 × 5 × 7 × 133 = 11,072,880
23 × 33 × 5 × 7 × 133 = 16,609,320
24 × 33 × 5 × 7 × 133 = 33,218,640

The final answer:
(scroll down)

33,218,640 has 320 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 12; 13; 14; 15; 16; 18; 20; 21; 24; 26; 27; 28; 30; 35; 36; 39; 40; 42; 45; 48; 52; 54; 56; 60; 63; 65; 70; 72; 78; 80; 84; 90; 91; 104; 105; 108; 112; 117; 120; 126; 130; 135; 140; 144; 156; 168; 169; 180; 182; 189; 195; 208; 210; 216; 234; 240; 252; 260; 270; 273; 280; 312; 315; 336; 338; 351; 360; 364; 378; 390; 420; 432; 455; 468; 504; 507; 520; 540; 546; 560; 585; 624; 630; 676; 702; 720; 728; 756; 780; 819; 840; 845; 910; 936; 945; 1,008; 1,014; 1,040; 1,080; 1,092; 1,170; 1,183; 1,260; 1,352; 1,365; 1,404; 1,456; 1,512; 1,521; 1,560; 1,638; 1,680; 1,690; 1,755; 1,820; 1,872; 1,890; 2,028; 2,160; 2,184; 2,197; 2,340; 2,366; 2,457; 2,520; 2,535; 2,704; 2,730; 2,808; 3,024; 3,042; 3,120; 3,276; 3,380; 3,510; 3,549; 3,640; 3,780; 4,056; 4,095; 4,368; 4,394; 4,563; 4,680; 4,732; 4,914; 5,040; 5,070; 5,460; 5,616; 5,915; 6,084; 6,552; 6,591; 6,760; 7,020; 7,098; 7,280; 7,560; 7,605; 8,112; 8,190; 8,788; 9,126; 9,360; 9,464; 9,828; 10,140; 10,647; 10,920; 10,985; 11,830; 12,168; 12,285; 13,104; 13,182; 13,520; 14,040; 14,196; 15,120; 15,210; 15,379; 16,380; 17,576; 17,745; 18,252; 18,928; 19,656; 19,773; 20,280; 21,294; 21,840; 21,970; 22,815; 23,660; 24,336; 24,570; 26,364; 28,080; 28,392; 30,420; 30,758; 31,941; 32,760; 32,955; 35,152; 35,490; 36,504; 39,312; 39,546; 40,560; 42,588; 43,940; 45,630; 46,137; 47,320; 49,140; 52,728; 53,235; 56,784; 59,319; 60,840; 61,516; 63,882; 65,520; 65,910; 70,980; 73,008; 76,895; 79,092; 85,176; 87,880; 91,260; 92,274; 94,640; 98,280; 98,865; 105,456; 106,470; 118,638; 121,680; 123,032; 127,764; 131,820; 138,411; 141,960; 153,790; 158,184; 159,705; 170,352; 175,760; 182,520; 184,548; 196,560; 197,730; 212,940; 230,685; 237,276; 246,064; 255,528; 263,640; 276,822; 283,920; 296,595; 307,580; 316,368; 319,410; 365,040; 369,096; 395,460; 415,233; 425,880; 461,370; 474,552; 511,056; 527,280; 553,644; 593,190; 615,160; 638,820; 692,055; 738,192; 790,920; 830,466; 851,760; 922,740; 949,104; 1,107,288; 1,186,380; 1,230,320; 1,277,640; 1,384,110; 1,581,840; 1,660,932; 1,845,480; 2,076,165; 2,214,576; 2,372,760; 2,555,280; 2,768,220; 3,321,864; 3,690,960; 4,152,330; 4,745,520; 5,536,440; 6,643,728; 8,304,660; 11,072,880; 16,609,320 and 33,218,640
out of which 5 prime factors: 2; 3; 5; 7 and 13
33,218,640 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 33,218,628?

» What are all the proper, improper and prime factors (divisors) of the number 33,218,650?


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".