Given the Number 3,432,000, Calculate (Find) All the Factors (All the Divisors) of the Number 3,432,000 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 3,432,000

1. Carry out the prime factorization of the number 3,432,000:

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

3,432,000 = 26 × 3 × 53 × 11 × 13
3,432,000 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 3,432,000

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
23 = 8
2 × 5 = 10
prime factor = 11
22 × 3 = 12
prime factor = 13
3 × 5 = 15
24 = 16
22 × 5 = 20
2 × 11 = 22
23 × 3 = 24
52 = 25
2 × 13 = 26
2 × 3 × 5 = 30
25 = 32
3 × 11 = 33
3 × 13 = 39
23 × 5 = 40
22 × 11 = 44
24 × 3 = 48
2 × 52 = 50
22 × 13 = 52
5 × 11 = 55
22 × 3 × 5 = 60
26 = 64
5 × 13 = 65
2 × 3 × 11 = 66
3 × 52 = 75
2 × 3 × 13 = 78
24 × 5 = 80
23 × 11 = 88
25 × 3 = 96
22 × 52 = 100
23 × 13 = 104
2 × 5 × 11 = 110
23 × 3 × 5 = 120
53 = 125
2 × 5 × 13 = 130
22 × 3 × 11 = 132
11 × 13 = 143
2 × 3 × 52 = 150
22 × 3 × 13 = 156
25 × 5 = 160
3 × 5 × 11 = 165
24 × 11 = 176
26 × 3 = 192
3 × 5 × 13 = 195
23 × 52 = 200
24 × 13 = 208
22 × 5 × 11 = 220
24 × 3 × 5 = 240
2 × 53 = 250
22 × 5 × 13 = 260
23 × 3 × 11 = 264
52 × 11 = 275
2 × 11 × 13 = 286
22 × 3 × 52 = 300
23 × 3 × 13 = 312
26 × 5 = 320
52 × 13 = 325
2 × 3 × 5 × 11 = 330
25 × 11 = 352
3 × 53 = 375
2 × 3 × 5 × 13 = 390
24 × 52 = 400
25 × 13 = 416
3 × 11 × 13 = 429
23 × 5 × 11 = 440
25 × 3 × 5 = 480
22 × 53 = 500
23 × 5 × 13 = 520
24 × 3 × 11 = 528
2 × 52 × 11 = 550
22 × 11 × 13 = 572
23 × 3 × 52 = 600
24 × 3 × 13 = 624
2 × 52 × 13 = 650
22 × 3 × 5 × 11 = 660
26 × 11 = 704
5 × 11 × 13 = 715
2 × 3 × 53 = 750
22 × 3 × 5 × 13 = 780
25 × 52 = 800
3 × 52 × 11 = 825
26 × 13 = 832
2 × 3 × 11 × 13 = 858
24 × 5 × 11 = 880
26 × 3 × 5 = 960
3 × 52 × 13 = 975
23 × 53 = 1,000
24 × 5 × 13 = 1,040
25 × 3 × 11 = 1,056
22 × 52 × 11 = 1,100
23 × 11 × 13 = 1,144
24 × 3 × 52 = 1,200
25 × 3 × 13 = 1,248
22 × 52 × 13 = 1,300
23 × 3 × 5 × 11 = 1,320
53 × 11 = 1,375
2 × 5 × 11 × 13 = 1,430
22 × 3 × 53 = 1,500
23 × 3 × 5 × 13 = 1,560
26 × 52 = 1,600
53 × 13 = 1,625
2 × 3 × 52 × 11 = 1,650
22 × 3 × 11 × 13 = 1,716
25 × 5 × 11 = 1,760
This list continues below...

... This list continues from above
2 × 3 × 52 × 13 = 1,950
24 × 53 = 2,000
25 × 5 × 13 = 2,080
26 × 3 × 11 = 2,112
3 × 5 × 11 × 13 = 2,145
23 × 52 × 11 = 2,200
24 × 11 × 13 = 2,288
25 × 3 × 52 = 2,400
26 × 3 × 13 = 2,496
23 × 52 × 13 = 2,600
24 × 3 × 5 × 11 = 2,640
2 × 53 × 11 = 2,750
22 × 5 × 11 × 13 = 2,860
23 × 3 × 53 = 3,000
24 × 3 × 5 × 13 = 3,120
2 × 53 × 13 = 3,250
22 × 3 × 52 × 11 = 3,300
23 × 3 × 11 × 13 = 3,432
26 × 5 × 11 = 3,520
52 × 11 × 13 = 3,575
22 × 3 × 52 × 13 = 3,900
25 × 53 = 4,000
3 × 53 × 11 = 4,125
26 × 5 × 13 = 4,160
2 × 3 × 5 × 11 × 13 = 4,290
24 × 52 × 11 = 4,400
25 × 11 × 13 = 4,576
26 × 3 × 52 = 4,800
3 × 53 × 13 = 4,875
24 × 52 × 13 = 5,200
25 × 3 × 5 × 11 = 5,280
22 × 53 × 11 = 5,500
23 × 5 × 11 × 13 = 5,720
24 × 3 × 53 = 6,000
25 × 3 × 5 × 13 = 6,240
22 × 53 × 13 = 6,500
23 × 3 × 52 × 11 = 6,600
24 × 3 × 11 × 13 = 6,864
2 × 52 × 11 × 13 = 7,150
23 × 3 × 52 × 13 = 7,800
26 × 53 = 8,000
2 × 3 × 53 × 11 = 8,250
22 × 3 × 5 × 11 × 13 = 8,580
25 × 52 × 11 = 8,800
26 × 11 × 13 = 9,152
2 × 3 × 53 × 13 = 9,750
25 × 52 × 13 = 10,400
26 × 3 × 5 × 11 = 10,560
3 × 52 × 11 × 13 = 10,725
23 × 53 × 11 = 11,000
24 × 5 × 11 × 13 = 11,440
25 × 3 × 53 = 12,000
26 × 3 × 5 × 13 = 12,480
23 × 53 × 13 = 13,000
24 × 3 × 52 × 11 = 13,200
25 × 3 × 11 × 13 = 13,728
22 × 52 × 11 × 13 = 14,300
24 × 3 × 52 × 13 = 15,600
22 × 3 × 53 × 11 = 16,500
23 × 3 × 5 × 11 × 13 = 17,160
26 × 52 × 11 = 17,600
53 × 11 × 13 = 17,875
22 × 3 × 53 × 13 = 19,500
26 × 52 × 13 = 20,800
2 × 3 × 52 × 11 × 13 = 21,450
24 × 53 × 11 = 22,000
25 × 5 × 11 × 13 = 22,880
26 × 3 × 53 = 24,000
24 × 53 × 13 = 26,000
25 × 3 × 52 × 11 = 26,400
26 × 3 × 11 × 13 = 27,456
23 × 52 × 11 × 13 = 28,600
25 × 3 × 52 × 13 = 31,200
23 × 3 × 53 × 11 = 33,000
24 × 3 × 5 × 11 × 13 = 34,320
2 × 53 × 11 × 13 = 35,750
23 × 3 × 53 × 13 = 39,000
22 × 3 × 52 × 11 × 13 = 42,900
25 × 53 × 11 = 44,000
26 × 5 × 11 × 13 = 45,760
25 × 53 × 13 = 52,000
26 × 3 × 52 × 11 = 52,800
3 × 53 × 11 × 13 = 53,625
24 × 52 × 11 × 13 = 57,200
26 × 3 × 52 × 13 = 62,400
24 × 3 × 53 × 11 = 66,000
25 × 3 × 5 × 11 × 13 = 68,640
22 × 53 × 11 × 13 = 71,500
24 × 3 × 53 × 13 = 78,000
23 × 3 × 52 × 11 × 13 = 85,800
26 × 53 × 11 = 88,000
26 × 53 × 13 = 104,000
2 × 3 × 53 × 11 × 13 = 107,250
25 × 52 × 11 × 13 = 114,400
25 × 3 × 53 × 11 = 132,000
26 × 3 × 5 × 11 × 13 = 137,280
23 × 53 × 11 × 13 = 143,000
25 × 3 × 53 × 13 = 156,000
24 × 3 × 52 × 11 × 13 = 171,600
22 × 3 × 53 × 11 × 13 = 214,500
26 × 52 × 11 × 13 = 228,800
26 × 3 × 53 × 11 = 264,000
24 × 53 × 11 × 13 = 286,000
26 × 3 × 53 × 13 = 312,000
25 × 3 × 52 × 11 × 13 = 343,200
23 × 3 × 53 × 11 × 13 = 429,000
25 × 53 × 11 × 13 = 572,000
26 × 3 × 52 × 11 × 13 = 686,400
24 × 3 × 53 × 11 × 13 = 858,000
26 × 53 × 11 × 13 = 1,144,000
25 × 3 × 53 × 11 × 13 = 1,716,000
26 × 3 × 53 × 11 × 13 = 3,432,000

The final answer:
(scroll down)

3,432,000 has 224 factors (divisors):
1; 2; 3; 4; 5; 6; 8; 10; 11; 12; 13; 15; 16; 20; 22; 24; 25; 26; 30; 32; 33; 39; 40; 44; 48; 50; 52; 55; 60; 64; 65; 66; 75; 78; 80; 88; 96; 100; 104; 110; 120; 125; 130; 132; 143; 150; 156; 160; 165; 176; 192; 195; 200; 208; 220; 240; 250; 260; 264; 275; 286; 300; 312; 320; 325; 330; 352; 375; 390; 400; 416; 429; 440; 480; 500; 520; 528; 550; 572; 600; 624; 650; 660; 704; 715; 750; 780; 800; 825; 832; 858; 880; 960; 975; 1,000; 1,040; 1,056; 1,100; 1,144; 1,200; 1,248; 1,300; 1,320; 1,375; 1,430; 1,500; 1,560; 1,600; 1,625; 1,650; 1,716; 1,760; 1,950; 2,000; 2,080; 2,112; 2,145; 2,200; 2,288; 2,400; 2,496; 2,600; 2,640; 2,750; 2,860; 3,000; 3,120; 3,250; 3,300; 3,432; 3,520; 3,575; 3,900; 4,000; 4,125; 4,160; 4,290; 4,400; 4,576; 4,800; 4,875; 5,200; 5,280; 5,500; 5,720; 6,000; 6,240; 6,500; 6,600; 6,864; 7,150; 7,800; 8,000; 8,250; 8,580; 8,800; 9,152; 9,750; 10,400; 10,560; 10,725; 11,000; 11,440; 12,000; 12,480; 13,000; 13,200; 13,728; 14,300; 15,600; 16,500; 17,160; 17,600; 17,875; 19,500; 20,800; 21,450; 22,000; 22,880; 24,000; 26,000; 26,400; 27,456; 28,600; 31,200; 33,000; 34,320; 35,750; 39,000; 42,900; 44,000; 45,760; 52,000; 52,800; 53,625; 57,200; 62,400; 66,000; 68,640; 71,500; 78,000; 85,800; 88,000; 104,000; 107,250; 114,400; 132,000; 137,280; 143,000; 156,000; 171,600; 214,500; 228,800; 264,000; 286,000; 312,000; 343,200; 429,000; 572,000; 686,400; 858,000; 1,144,000; 1,716,000 and 3,432,000
out of which 5 prime factors: 2; 3; 5; 11 and 13
3,432,000 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 3,431,986?

» What are all the proper, improper and prime factors (divisors) of the number 3,432,013?


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".