Given the Number 42,755,850, Calculate (Find) All the Factors (All the Divisors) of the Number 42,755,850 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 42,755,850

1. Carry out the prime factorization of the number 42,755,850:

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


42,755,850 = 2 × 37 × 52 × 17 × 23
42,755,850 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 42,755,850

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
prime factor = 5
2 × 3 = 6
32 = 9
2 × 5 = 10
3 × 5 = 15
prime factor = 17
2 × 32 = 18
prime factor = 23
52 = 25
33 = 27
2 × 3 × 5 = 30
2 × 17 = 34
32 × 5 = 45
2 × 23 = 46
2 × 52 = 50
3 × 17 = 51
2 × 33 = 54
3 × 23 = 69
3 × 52 = 75
34 = 81
5 × 17 = 85
2 × 32 × 5 = 90
2 × 3 × 17 = 102
5 × 23 = 115
33 × 5 = 135
2 × 3 × 23 = 138
2 × 3 × 52 = 150
32 × 17 = 153
2 × 34 = 162
2 × 5 × 17 = 170
32 × 23 = 207
32 × 52 = 225
2 × 5 × 23 = 230
35 = 243
3 × 5 × 17 = 255
2 × 33 × 5 = 270
2 × 32 × 17 = 306
3 × 5 × 23 = 345
17 × 23 = 391
34 × 5 = 405
2 × 32 × 23 = 414
52 × 17 = 425
2 × 32 × 52 = 450
33 × 17 = 459
2 × 35 = 486
2 × 3 × 5 × 17 = 510
52 × 23 = 575
33 × 23 = 621
33 × 52 = 675
2 × 3 × 5 × 23 = 690
36 = 729
32 × 5 × 17 = 765
2 × 17 × 23 = 782
2 × 34 × 5 = 810
2 × 52 × 17 = 850
2 × 33 × 17 = 918
32 × 5 × 23 = 1,035
2 × 52 × 23 = 1,150
3 × 17 × 23 = 1,173
35 × 5 = 1,215
2 × 33 × 23 = 1,242
3 × 52 × 17 = 1,275
2 × 33 × 52 = 1,350
34 × 17 = 1,377
2 × 36 = 1,458
2 × 32 × 5 × 17 = 1,530
3 × 52 × 23 = 1,725
34 × 23 = 1,863
5 × 17 × 23 = 1,955
34 × 52 = 2,025
2 × 32 × 5 × 23 = 2,070
37 = 2,187
33 × 5 × 17 = 2,295
2 × 3 × 17 × 23 = 2,346
2 × 35 × 5 = 2,430
2 × 3 × 52 × 17 = 2,550
2 × 34 × 17 = 2,754
33 × 5 × 23 = 3,105
2 × 3 × 52 × 23 = 3,450
32 × 17 × 23 = 3,519
36 × 5 = 3,645
2 × 34 × 23 = 3,726
32 × 52 × 17 = 3,825
2 × 5 × 17 × 23 = 3,910
2 × 34 × 52 = 4,050
35 × 17 = 4,131
2 × 37 = 4,374
2 × 33 × 5 × 17 = 4,590
32 × 52 × 23 = 5,175
35 × 23 = 5,589
3 × 5 × 17 × 23 = 5,865
35 × 52 = 6,075
2 × 33 × 5 × 23 = 6,210
This list continues below...

... This list continues from above
34 × 5 × 17 = 6,885
2 × 32 × 17 × 23 = 7,038
2 × 36 × 5 = 7,290
2 × 32 × 52 × 17 = 7,650
2 × 35 × 17 = 8,262
34 × 5 × 23 = 9,315
52 × 17 × 23 = 9,775
2 × 32 × 52 × 23 = 10,350
33 × 17 × 23 = 10,557
37 × 5 = 10,935
2 × 35 × 23 = 11,178
33 × 52 × 17 = 11,475
2 × 3 × 5 × 17 × 23 = 11,730
2 × 35 × 52 = 12,150
36 × 17 = 12,393
2 × 34 × 5 × 17 = 13,770
33 × 52 × 23 = 15,525
36 × 23 = 16,767
32 × 5 × 17 × 23 = 17,595
36 × 52 = 18,225
2 × 34 × 5 × 23 = 18,630
2 × 52 × 17 × 23 = 19,550
35 × 5 × 17 = 20,655
2 × 33 × 17 × 23 = 21,114
2 × 37 × 5 = 21,870
2 × 33 × 52 × 17 = 22,950
2 × 36 × 17 = 24,786
35 × 5 × 23 = 27,945
3 × 52 × 17 × 23 = 29,325
2 × 33 × 52 × 23 = 31,050
34 × 17 × 23 = 31,671
2 × 36 × 23 = 33,534
34 × 52 × 17 = 34,425
2 × 32 × 5 × 17 × 23 = 35,190
2 × 36 × 52 = 36,450
37 × 17 = 37,179
2 × 35 × 5 × 17 = 41,310
34 × 52 × 23 = 46,575
37 × 23 = 50,301
33 × 5 × 17 × 23 = 52,785
37 × 52 = 54,675
2 × 35 × 5 × 23 = 55,890
2 × 3 × 52 × 17 × 23 = 58,650
36 × 5 × 17 = 61,965
2 × 34 × 17 × 23 = 63,342
2 × 34 × 52 × 17 = 68,850
2 × 37 × 17 = 74,358
36 × 5 × 23 = 83,835
32 × 52 × 17 × 23 = 87,975
2 × 34 × 52 × 23 = 93,150
35 × 17 × 23 = 95,013
2 × 37 × 23 = 100,602
35 × 52 × 17 = 103,275
2 × 33 × 5 × 17 × 23 = 105,570
2 × 37 × 52 = 109,350
2 × 36 × 5 × 17 = 123,930
35 × 52 × 23 = 139,725
34 × 5 × 17 × 23 = 158,355
2 × 36 × 5 × 23 = 167,670
2 × 32 × 52 × 17 × 23 = 175,950
37 × 5 × 17 = 185,895
2 × 35 × 17 × 23 = 190,026
2 × 35 × 52 × 17 = 206,550
37 × 5 × 23 = 251,505
33 × 52 × 17 × 23 = 263,925
2 × 35 × 52 × 23 = 279,450
36 × 17 × 23 = 285,039
36 × 52 × 17 = 309,825
2 × 34 × 5 × 17 × 23 = 316,710
2 × 37 × 5 × 17 = 371,790
36 × 52 × 23 = 419,175
35 × 5 × 17 × 23 = 475,065
2 × 37 × 5 × 23 = 503,010
2 × 33 × 52 × 17 × 23 = 527,850
2 × 36 × 17 × 23 = 570,078
2 × 36 × 52 × 17 = 619,650
34 × 52 × 17 × 23 = 791,775
2 × 36 × 52 × 23 = 838,350
37 × 17 × 23 = 855,117
37 × 52 × 17 = 929,475
2 × 35 × 5 × 17 × 23 = 950,130
37 × 52 × 23 = 1,257,525
36 × 5 × 17 × 23 = 1,425,195
2 × 34 × 52 × 17 × 23 = 1,583,550
2 × 37 × 17 × 23 = 1,710,234
2 × 37 × 52 × 17 = 1,858,950
35 × 52 × 17 × 23 = 2,375,325
2 × 37 × 52 × 23 = 2,515,050
2 × 36 × 5 × 17 × 23 = 2,850,390
37 × 5 × 17 × 23 = 4,275,585
2 × 35 × 52 × 17 × 23 = 4,750,650
36 × 52 × 17 × 23 = 7,125,975
2 × 37 × 5 × 17 × 23 = 8,551,170
2 × 36 × 52 × 17 × 23 = 14,251,950
37 × 52 × 17 × 23 = 21,377,925
2 × 37 × 52 × 17 × 23 = 42,755,850

The final answer:
(scroll down)

42,755,850 has 192 factors (divisors):
1; 2; 3; 5; 6; 9; 10; 15; 17; 18; 23; 25; 27; 30; 34; 45; 46; 50; 51; 54; 69; 75; 81; 85; 90; 102; 115; 135; 138; 150; 153; 162; 170; 207; 225; 230; 243; 255; 270; 306; 345; 391; 405; 414; 425; 450; 459; 486; 510; 575; 621; 675; 690; 729; 765; 782; 810; 850; 918; 1,035; 1,150; 1,173; 1,215; 1,242; 1,275; 1,350; 1,377; 1,458; 1,530; 1,725; 1,863; 1,955; 2,025; 2,070; 2,187; 2,295; 2,346; 2,430; 2,550; 2,754; 3,105; 3,450; 3,519; 3,645; 3,726; 3,825; 3,910; 4,050; 4,131; 4,374; 4,590; 5,175; 5,589; 5,865; 6,075; 6,210; 6,885; 7,038; 7,290; 7,650; 8,262; 9,315; 9,775; 10,350; 10,557; 10,935; 11,178; 11,475; 11,730; 12,150; 12,393; 13,770; 15,525; 16,767; 17,595; 18,225; 18,630; 19,550; 20,655; 21,114; 21,870; 22,950; 24,786; 27,945; 29,325; 31,050; 31,671; 33,534; 34,425; 35,190; 36,450; 37,179; 41,310; 46,575; 50,301; 52,785; 54,675; 55,890; 58,650; 61,965; 63,342; 68,850; 74,358; 83,835; 87,975; 93,150; 95,013; 100,602; 103,275; 105,570; 109,350; 123,930; 139,725; 158,355; 167,670; 175,950; 185,895; 190,026; 206,550; 251,505; 263,925; 279,450; 285,039; 309,825; 316,710; 371,790; 419,175; 475,065; 503,010; 527,850; 570,078; 619,650; 791,775; 838,350; 855,117; 929,475; 950,130; 1,257,525; 1,425,195; 1,583,550; 1,710,234; 1,858,950; 2,375,325; 2,515,050; 2,850,390; 4,275,585; 4,750,650; 7,125,975; 8,551,170; 14,251,950; 21,377,925 and 42,755,850
out of which 5 prime factors: 2; 3; 5; 17 and 23
42,755,850 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

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".