Given the Number 35,501,760, Calculate (Find) All the Factors (All the Divisors) of the Number 35,501,760 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 35,501,760

1. Carry out the prime factorization of the number 35,501,760:

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


35,501,760 = 26 × 33 × 5 × 7 × 587
35,501,760 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 35,501,760

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
2 × 7 = 14
3 × 5 = 15
24 = 16
2 × 32 = 18
22 × 5 = 20
3 × 7 = 21
23 × 3 = 24
33 = 27
22 × 7 = 28
2 × 3 × 5 = 30
25 = 32
5 × 7 = 35
22 × 32 = 36
23 × 5 = 40
2 × 3 × 7 = 42
32 × 5 = 45
24 × 3 = 48
2 × 33 = 54
23 × 7 = 56
22 × 3 × 5 = 60
32 × 7 = 63
26 = 64
2 × 5 × 7 = 70
23 × 32 = 72
24 × 5 = 80
22 × 3 × 7 = 84
2 × 32 × 5 = 90
25 × 3 = 96
3 × 5 × 7 = 105
22 × 33 = 108
24 × 7 = 112
23 × 3 × 5 = 120
2 × 32 × 7 = 126
33 × 5 = 135
22 × 5 × 7 = 140
24 × 32 = 144
25 × 5 = 160
23 × 3 × 7 = 168
22 × 32 × 5 = 180
33 × 7 = 189
26 × 3 = 192
2 × 3 × 5 × 7 = 210
23 × 33 = 216
25 × 7 = 224
24 × 3 × 5 = 240
22 × 32 × 7 = 252
2 × 33 × 5 = 270
23 × 5 × 7 = 280
25 × 32 = 288
32 × 5 × 7 = 315
26 × 5 = 320
24 × 3 × 7 = 336
23 × 32 × 5 = 360
2 × 33 × 7 = 378
22 × 3 × 5 × 7 = 420
24 × 33 = 432
26 × 7 = 448
25 × 3 × 5 = 480
23 × 32 × 7 = 504
22 × 33 × 5 = 540
24 × 5 × 7 = 560
26 × 32 = 576
prime factor = 587
2 × 32 × 5 × 7 = 630
25 × 3 × 7 = 672
24 × 32 × 5 = 720
22 × 33 × 7 = 756
23 × 3 × 5 × 7 = 840
25 × 33 = 864
33 × 5 × 7 = 945
26 × 3 × 5 = 960
24 × 32 × 7 = 1,008
23 × 33 × 5 = 1,080
25 × 5 × 7 = 1,120
2 × 587 = 1,174
22 × 32 × 5 × 7 = 1,260
26 × 3 × 7 = 1,344
25 × 32 × 5 = 1,440
23 × 33 × 7 = 1,512
24 × 3 × 5 × 7 = 1,680
26 × 33 = 1,728
3 × 587 = 1,761
2 × 33 × 5 × 7 = 1,890
25 × 32 × 7 = 2,016
24 × 33 × 5 = 2,160
26 × 5 × 7 = 2,240
22 × 587 = 2,348
23 × 32 × 5 × 7 = 2,520
26 × 32 × 5 = 2,880
5 × 587 = 2,935
24 × 33 × 7 = 3,024
25 × 3 × 5 × 7 = 3,360
2 × 3 × 587 = 3,522
22 × 33 × 5 × 7 = 3,780
26 × 32 × 7 = 4,032
7 × 587 = 4,109
25 × 33 × 5 = 4,320
23 × 587 = 4,696
24 × 32 × 5 × 7 = 5,040
32 × 587 = 5,283
2 × 5 × 587 = 5,870
This list continues below...

... This list continues from above
25 × 33 × 7 = 6,048
26 × 3 × 5 × 7 = 6,720
22 × 3 × 587 = 7,044
23 × 33 × 5 × 7 = 7,560
2 × 7 × 587 = 8,218
26 × 33 × 5 = 8,640
3 × 5 × 587 = 8,805
24 × 587 = 9,392
25 × 32 × 5 × 7 = 10,080
2 × 32 × 587 = 10,566
22 × 5 × 587 = 11,740
26 × 33 × 7 = 12,096
3 × 7 × 587 = 12,327
23 × 3 × 587 = 14,088
24 × 33 × 5 × 7 = 15,120
33 × 587 = 15,849
22 × 7 × 587 = 16,436
2 × 3 × 5 × 587 = 17,610
25 × 587 = 18,784
26 × 32 × 5 × 7 = 20,160
5 × 7 × 587 = 20,545
22 × 32 × 587 = 21,132
23 × 5 × 587 = 23,480
2 × 3 × 7 × 587 = 24,654
32 × 5 × 587 = 26,415
24 × 3 × 587 = 28,176
25 × 33 × 5 × 7 = 30,240
2 × 33 × 587 = 31,698
23 × 7 × 587 = 32,872
22 × 3 × 5 × 587 = 35,220
32 × 7 × 587 = 36,981
26 × 587 = 37,568
2 × 5 × 7 × 587 = 41,090
23 × 32 × 587 = 42,264
24 × 5 × 587 = 46,960
22 × 3 × 7 × 587 = 49,308
2 × 32 × 5 × 587 = 52,830
25 × 3 × 587 = 56,352
26 × 33 × 5 × 7 = 60,480
3 × 5 × 7 × 587 = 61,635
22 × 33 × 587 = 63,396
24 × 7 × 587 = 65,744
23 × 3 × 5 × 587 = 70,440
2 × 32 × 7 × 587 = 73,962
33 × 5 × 587 = 79,245
22 × 5 × 7 × 587 = 82,180
24 × 32 × 587 = 84,528
25 × 5 × 587 = 93,920
23 × 3 × 7 × 587 = 98,616
22 × 32 × 5 × 587 = 105,660
33 × 7 × 587 = 110,943
26 × 3 × 587 = 112,704
2 × 3 × 5 × 7 × 587 = 123,270
23 × 33 × 587 = 126,792
25 × 7 × 587 = 131,488
24 × 3 × 5 × 587 = 140,880
22 × 32 × 7 × 587 = 147,924
2 × 33 × 5 × 587 = 158,490
23 × 5 × 7 × 587 = 164,360
25 × 32 × 587 = 169,056
32 × 5 × 7 × 587 = 184,905
26 × 5 × 587 = 187,840
24 × 3 × 7 × 587 = 197,232
23 × 32 × 5 × 587 = 211,320
2 × 33 × 7 × 587 = 221,886
22 × 3 × 5 × 7 × 587 = 246,540
24 × 33 × 587 = 253,584
26 × 7 × 587 = 262,976
25 × 3 × 5 × 587 = 281,760
23 × 32 × 7 × 587 = 295,848
22 × 33 × 5 × 587 = 316,980
24 × 5 × 7 × 587 = 328,720
26 × 32 × 587 = 338,112
2 × 32 × 5 × 7 × 587 = 369,810
25 × 3 × 7 × 587 = 394,464
24 × 32 × 5 × 587 = 422,640
22 × 33 × 7 × 587 = 443,772
23 × 3 × 5 × 7 × 587 = 493,080
25 × 33 × 587 = 507,168
33 × 5 × 7 × 587 = 554,715
26 × 3 × 5 × 587 = 563,520
24 × 32 × 7 × 587 = 591,696
23 × 33 × 5 × 587 = 633,960
25 × 5 × 7 × 587 = 657,440
22 × 32 × 5 × 7 × 587 = 739,620
26 × 3 × 7 × 587 = 788,928
25 × 32 × 5 × 587 = 845,280
23 × 33 × 7 × 587 = 887,544
24 × 3 × 5 × 7 × 587 = 986,160
26 × 33 × 587 = 1,014,336
2 × 33 × 5 × 7 × 587 = 1,109,430
25 × 32 × 7 × 587 = 1,183,392
24 × 33 × 5 × 587 = 1,267,920
26 × 5 × 7 × 587 = 1,314,880
23 × 32 × 5 × 7 × 587 = 1,479,240
26 × 32 × 5 × 587 = 1,690,560
24 × 33 × 7 × 587 = 1,775,088
25 × 3 × 5 × 7 × 587 = 1,972,320
22 × 33 × 5 × 7 × 587 = 2,218,860
26 × 32 × 7 × 587 = 2,366,784
25 × 33 × 5 × 587 = 2,535,840
24 × 32 × 5 × 7 × 587 = 2,958,480
25 × 33 × 7 × 587 = 3,550,176
26 × 3 × 5 × 7 × 587 = 3,944,640
23 × 33 × 5 × 7 × 587 = 4,437,720
26 × 33 × 5 × 587 = 5,071,680
25 × 32 × 5 × 7 × 587 = 5,916,960
26 × 33 × 7 × 587 = 7,100,352
24 × 33 × 5 × 7 × 587 = 8,875,440
26 × 32 × 5 × 7 × 587 = 11,833,920
25 × 33 × 5 × 7 × 587 = 17,750,880
26 × 33 × 5 × 7 × 587 = 35,501,760

The final answer:
(scroll down)

35,501,760 has 224 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 12; 14; 15; 16; 18; 20; 21; 24; 27; 28; 30; 32; 35; 36; 40; 42; 45; 48; 54; 56; 60; 63; 64; 70; 72; 80; 84; 90; 96; 105; 108; 112; 120; 126; 135; 140; 144; 160; 168; 180; 189; 192; 210; 216; 224; 240; 252; 270; 280; 288; 315; 320; 336; 360; 378; 420; 432; 448; 480; 504; 540; 560; 576; 587; 630; 672; 720; 756; 840; 864; 945; 960; 1,008; 1,080; 1,120; 1,174; 1,260; 1,344; 1,440; 1,512; 1,680; 1,728; 1,761; 1,890; 2,016; 2,160; 2,240; 2,348; 2,520; 2,880; 2,935; 3,024; 3,360; 3,522; 3,780; 4,032; 4,109; 4,320; 4,696; 5,040; 5,283; 5,870; 6,048; 6,720; 7,044; 7,560; 8,218; 8,640; 8,805; 9,392; 10,080; 10,566; 11,740; 12,096; 12,327; 14,088; 15,120; 15,849; 16,436; 17,610; 18,784; 20,160; 20,545; 21,132; 23,480; 24,654; 26,415; 28,176; 30,240; 31,698; 32,872; 35,220; 36,981; 37,568; 41,090; 42,264; 46,960; 49,308; 52,830; 56,352; 60,480; 61,635; 63,396; 65,744; 70,440; 73,962; 79,245; 82,180; 84,528; 93,920; 98,616; 105,660; 110,943; 112,704; 123,270; 126,792; 131,488; 140,880; 147,924; 158,490; 164,360; 169,056; 184,905; 187,840; 197,232; 211,320; 221,886; 246,540; 253,584; 262,976; 281,760; 295,848; 316,980; 328,720; 338,112; 369,810; 394,464; 422,640; 443,772; 493,080; 507,168; 554,715; 563,520; 591,696; 633,960; 657,440; 739,620; 788,928; 845,280; 887,544; 986,160; 1,014,336; 1,109,430; 1,183,392; 1,267,920; 1,314,880; 1,479,240; 1,690,560; 1,775,088; 1,972,320; 2,218,860; 2,366,784; 2,535,840; 2,958,480; 3,550,176; 3,944,640; 4,437,720; 5,071,680; 5,916,960; 7,100,352; 8,875,440; 11,833,920; 17,750,880 and 35,501,760
out of which 5 prime factors: 2; 3; 5; 7 and 587
35,501,760 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.


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".