Given the Number 1,332,800, Calculate (Find) All the Factors (All the Divisors) of the Number 1,332,800 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 1,332,800

1. Carry out the prime factorization of the number 1,332,800:

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

1,332,800 = 26 × 52 × 72 × 17
1,332,800 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 1,332,800

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
22 = 4
prime factor = 5
prime factor = 7
23 = 8
2 × 5 = 10
2 × 7 = 14
24 = 16
prime factor = 17
22 × 5 = 20
52 = 25
22 × 7 = 28
25 = 32
2 × 17 = 34
5 × 7 = 35
23 × 5 = 40
72 = 49
2 × 52 = 50
23 × 7 = 56
26 = 64
22 × 17 = 68
2 × 5 × 7 = 70
24 × 5 = 80
5 × 17 = 85
2 × 72 = 98
22 × 52 = 100
24 × 7 = 112
7 × 17 = 119
23 × 17 = 136
22 × 5 × 7 = 140
25 × 5 = 160
2 × 5 × 17 = 170
52 × 7 = 175
22 × 72 = 196
23 × 52 = 200
25 × 7 = 224
2 × 7 × 17 = 238
5 × 72 = 245
24 × 17 = 272
23 × 5 × 7 = 280
26 × 5 = 320
22 × 5 × 17 = 340
2 × 52 × 7 = 350
23 × 72 = 392
24 × 52 = 400
52 × 17 = 425
26 × 7 = 448
22 × 7 × 17 = 476
2 × 5 × 72 = 490
25 × 17 = 544
24 × 5 × 7 = 560
5 × 7 × 17 = 595
23 × 5 × 17 = 680
22 × 52 × 7 = 700
24 × 72 = 784
25 × 52 = 800
72 × 17 = 833
2 × 52 × 17 = 850
23 × 7 × 17 = 952
22 × 5 × 72 = 980
26 × 17 = 1,088
25 × 5 × 7 = 1,120
This list continues below...

... This list continues from above
2 × 5 × 7 × 17 = 1,190
52 × 72 = 1,225
24 × 5 × 17 = 1,360
23 × 52 × 7 = 1,400
25 × 72 = 1,568
26 × 52 = 1,600
2 × 72 × 17 = 1,666
22 × 52 × 17 = 1,700
24 × 7 × 17 = 1,904
23 × 5 × 72 = 1,960
26 × 5 × 7 = 2,240
22 × 5 × 7 × 17 = 2,380
2 × 52 × 72 = 2,450
25 × 5 × 17 = 2,720
24 × 52 × 7 = 2,800
52 × 7 × 17 = 2,975
26 × 72 = 3,136
22 × 72 × 17 = 3,332
23 × 52 × 17 = 3,400
25 × 7 × 17 = 3,808
24 × 5 × 72 = 3,920
5 × 72 × 17 = 4,165
23 × 5 × 7 × 17 = 4,760
22 × 52 × 72 = 4,900
26 × 5 × 17 = 5,440
25 × 52 × 7 = 5,600
2 × 52 × 7 × 17 = 5,950
23 × 72 × 17 = 6,664
24 × 52 × 17 = 6,800
26 × 7 × 17 = 7,616
25 × 5 × 72 = 7,840
2 × 5 × 72 × 17 = 8,330
24 × 5 × 7 × 17 = 9,520
23 × 52 × 72 = 9,800
26 × 52 × 7 = 11,200
22 × 52 × 7 × 17 = 11,900
24 × 72 × 17 = 13,328
25 × 52 × 17 = 13,600
26 × 5 × 72 = 15,680
22 × 5 × 72 × 17 = 16,660
25 × 5 × 7 × 17 = 19,040
24 × 52 × 72 = 19,600
52 × 72 × 17 = 20,825
23 × 52 × 7 × 17 = 23,800
25 × 72 × 17 = 26,656
26 × 52 × 17 = 27,200
23 × 5 × 72 × 17 = 33,320
26 × 5 × 7 × 17 = 38,080
25 × 52 × 72 = 39,200
2 × 52 × 72 × 17 = 41,650
24 × 52 × 7 × 17 = 47,600
26 × 72 × 17 = 53,312
24 × 5 × 72 × 17 = 66,640
26 × 52 × 72 = 78,400
22 × 52 × 72 × 17 = 83,300
25 × 52 × 7 × 17 = 95,200
25 × 5 × 72 × 17 = 133,280
23 × 52 × 72 × 17 = 166,600
26 × 52 × 7 × 17 = 190,400
26 × 5 × 72 × 17 = 266,560
24 × 52 × 72 × 17 = 333,200
25 × 52 × 72 × 17 = 666,400
26 × 52 × 72 × 17 = 1,332,800

The final answer:
(scroll down)

1,332,800 has 126 factors (divisors):
1; 2; 4; 5; 7; 8; 10; 14; 16; 17; 20; 25; 28; 32; 34; 35; 40; 49; 50; 56; 64; 68; 70; 80; 85; 98; 100; 112; 119; 136; 140; 160; 170; 175; 196; 200; 224; 238; 245; 272; 280; 320; 340; 350; 392; 400; 425; 448; 476; 490; 544; 560; 595; 680; 700; 784; 800; 833; 850; 952; 980; 1,088; 1,120; 1,190; 1,225; 1,360; 1,400; 1,568; 1,600; 1,666; 1,700; 1,904; 1,960; 2,240; 2,380; 2,450; 2,720; 2,800; 2,975; 3,136; 3,332; 3,400; 3,808; 3,920; 4,165; 4,760; 4,900; 5,440; 5,600; 5,950; 6,664; 6,800; 7,616; 7,840; 8,330; 9,520; 9,800; 11,200; 11,900; 13,328; 13,600; 15,680; 16,660; 19,040; 19,600; 20,825; 23,800; 26,656; 27,200; 33,320; 38,080; 39,200; 41,650; 47,600; 53,312; 66,640; 78,400; 83,300; 95,200; 133,280; 166,600; 190,400; 266,560; 333,200; 666,400 and 1,332,800
out of which 4 prime factors: 2; 5; 7 and 17
1,332,800 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 1,332,787?

» What are all the proper, improper and prime factors (divisors) of the number 1,332,810?


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".