Given the Number 1,999,200, Calculate (Find) All the Factors (All the Divisors) of the Number 1,999,200 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 1,999,200

1. Carry out the prime factorization of the number 1,999,200:

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

1,999,200 = 25 × 3 × 52 × 72 × 17
1,999,200 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 1,999,200

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
2 × 5 = 10
22 × 3 = 12
2 × 7 = 14
3 × 5 = 15
24 = 16
prime factor = 17
22 × 5 = 20
3 × 7 = 21
23 × 3 = 24
52 = 25
22 × 7 = 28
2 × 3 × 5 = 30
25 = 32
2 × 17 = 34
5 × 7 = 35
23 × 5 = 40
2 × 3 × 7 = 42
24 × 3 = 48
72 = 49
2 × 52 = 50
3 × 17 = 51
23 × 7 = 56
22 × 3 × 5 = 60
22 × 17 = 68
2 × 5 × 7 = 70
3 × 52 = 75
24 × 5 = 80
22 × 3 × 7 = 84
5 × 17 = 85
25 × 3 = 96
2 × 72 = 98
22 × 52 = 100
2 × 3 × 17 = 102
3 × 5 × 7 = 105
24 × 7 = 112
7 × 17 = 119
23 × 3 × 5 = 120
23 × 17 = 136
22 × 5 × 7 = 140
3 × 72 = 147
2 × 3 × 52 = 150
25 × 5 = 160
23 × 3 × 7 = 168
2 × 5 × 17 = 170
52 × 7 = 175
22 × 72 = 196
23 × 52 = 200
22 × 3 × 17 = 204
2 × 3 × 5 × 7 = 210
25 × 7 = 224
2 × 7 × 17 = 238
24 × 3 × 5 = 240
5 × 72 = 245
3 × 5 × 17 = 255
24 × 17 = 272
23 × 5 × 7 = 280
2 × 3 × 72 = 294
22 × 3 × 52 = 300
24 × 3 × 7 = 336
22 × 5 × 17 = 340
2 × 52 × 7 = 350
3 × 7 × 17 = 357
23 × 72 = 392
24 × 52 = 400
23 × 3 × 17 = 408
22 × 3 × 5 × 7 = 420
52 × 17 = 425
22 × 7 × 17 = 476
25 × 3 × 5 = 480
2 × 5 × 72 = 490
2 × 3 × 5 × 17 = 510
3 × 52 × 7 = 525
25 × 17 = 544
24 × 5 × 7 = 560
22 × 3 × 72 = 588
5 × 7 × 17 = 595
23 × 3 × 52 = 600
25 × 3 × 7 = 672
23 × 5 × 17 = 680
22 × 52 × 7 = 700
2 × 3 × 7 × 17 = 714
3 × 5 × 72 = 735
24 × 72 = 784
25 × 52 = 800
24 × 3 × 17 = 816
72 × 17 = 833
23 × 3 × 5 × 7 = 840
2 × 52 × 17 = 850
23 × 7 × 17 = 952
22 × 5 × 72 = 980
22 × 3 × 5 × 17 = 1,020
2 × 3 × 52 × 7 = 1,050
25 × 5 × 7 = 1,120
23 × 3 × 72 = 1,176
2 × 5 × 7 × 17 = 1,190
24 × 3 × 52 = 1,200
52 × 72 = 1,225
3 × 52 × 17 = 1,275
24 × 5 × 17 = 1,360
23 × 52 × 7 = 1,400
This list continues below...

... This list continues from above
22 × 3 × 7 × 17 = 1,428
2 × 3 × 5 × 72 = 1,470
25 × 72 = 1,568
25 × 3 × 17 = 1,632
2 × 72 × 17 = 1,666
24 × 3 × 5 × 7 = 1,680
22 × 52 × 17 = 1,700
3 × 5 × 7 × 17 = 1,785
24 × 7 × 17 = 1,904
23 × 5 × 72 = 1,960
23 × 3 × 5 × 17 = 2,040
22 × 3 × 52 × 7 = 2,100
24 × 3 × 72 = 2,352
22 × 5 × 7 × 17 = 2,380
25 × 3 × 52 = 2,400
2 × 52 × 72 = 2,450
3 × 72 × 17 = 2,499
2 × 3 × 52 × 17 = 2,550
25 × 5 × 17 = 2,720
24 × 52 × 7 = 2,800
23 × 3 × 7 × 17 = 2,856
22 × 3 × 5 × 72 = 2,940
52 × 7 × 17 = 2,975
22 × 72 × 17 = 3,332
25 × 3 × 5 × 7 = 3,360
23 × 52 × 17 = 3,400
2 × 3 × 5 × 7 × 17 = 3,570
3 × 52 × 72 = 3,675
25 × 7 × 17 = 3,808
24 × 5 × 72 = 3,920
24 × 3 × 5 × 17 = 4,080
5 × 72 × 17 = 4,165
23 × 3 × 52 × 7 = 4,200
25 × 3 × 72 = 4,704
23 × 5 × 7 × 17 = 4,760
22 × 52 × 72 = 4,900
2 × 3 × 72 × 17 = 4,998
22 × 3 × 52 × 17 = 5,100
25 × 52 × 7 = 5,600
24 × 3 × 7 × 17 = 5,712
23 × 3 × 5 × 72 = 5,880
2 × 52 × 7 × 17 = 5,950
23 × 72 × 17 = 6,664
24 × 52 × 17 = 6,800
22 × 3 × 5 × 7 × 17 = 7,140
2 × 3 × 52 × 72 = 7,350
25 × 5 × 72 = 7,840
25 × 3 × 5 × 17 = 8,160
2 × 5 × 72 × 17 = 8,330
24 × 3 × 52 × 7 = 8,400
3 × 52 × 7 × 17 = 8,925
24 × 5 × 7 × 17 = 9,520
23 × 52 × 72 = 9,800
22 × 3 × 72 × 17 = 9,996
23 × 3 × 52 × 17 = 10,200
25 × 3 × 7 × 17 = 11,424
24 × 3 × 5 × 72 = 11,760
22 × 52 × 7 × 17 = 11,900
3 × 5 × 72 × 17 = 12,495
24 × 72 × 17 = 13,328
25 × 52 × 17 = 13,600
23 × 3 × 5 × 7 × 17 = 14,280
22 × 3 × 52 × 72 = 14,700
22 × 5 × 72 × 17 = 16,660
25 × 3 × 52 × 7 = 16,800
2 × 3 × 52 × 7 × 17 = 17,850
25 × 5 × 7 × 17 = 19,040
24 × 52 × 72 = 19,600
23 × 3 × 72 × 17 = 19,992
24 × 3 × 52 × 17 = 20,400
52 × 72 × 17 = 20,825
25 × 3 × 5 × 72 = 23,520
23 × 52 × 7 × 17 = 23,800
2 × 3 × 5 × 72 × 17 = 24,990
25 × 72 × 17 = 26,656
24 × 3 × 5 × 7 × 17 = 28,560
23 × 3 × 52 × 72 = 29,400
23 × 5 × 72 × 17 = 33,320
22 × 3 × 52 × 7 × 17 = 35,700
25 × 52 × 72 = 39,200
24 × 3 × 72 × 17 = 39,984
25 × 3 × 52 × 17 = 40,800
2 × 52 × 72 × 17 = 41,650
24 × 52 × 7 × 17 = 47,600
22 × 3 × 5 × 72 × 17 = 49,980
25 × 3 × 5 × 7 × 17 = 57,120
24 × 3 × 52 × 72 = 58,800
3 × 52 × 72 × 17 = 62,475
24 × 5 × 72 × 17 = 66,640
23 × 3 × 52 × 7 × 17 = 71,400
25 × 3 × 72 × 17 = 79,968
22 × 52 × 72 × 17 = 83,300
25 × 52 × 7 × 17 = 95,200
23 × 3 × 5 × 72 × 17 = 99,960
25 × 3 × 52 × 72 = 117,600
2 × 3 × 52 × 72 × 17 = 124,950
25 × 5 × 72 × 17 = 133,280
24 × 3 × 52 × 7 × 17 = 142,800
23 × 52 × 72 × 17 = 166,600
24 × 3 × 5 × 72 × 17 = 199,920
22 × 3 × 52 × 72 × 17 = 249,900
25 × 3 × 52 × 7 × 17 = 285,600
24 × 52 × 72 × 17 = 333,200
25 × 3 × 5 × 72 × 17 = 399,840
23 × 3 × 52 × 72 × 17 = 499,800
25 × 52 × 72 × 17 = 666,400
24 × 3 × 52 × 72 × 17 = 999,600
25 × 3 × 52 × 72 × 17 = 1,999,200

The final answer:
(scroll down)

1,999,200 has 216 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 8; 10; 12; 14; 15; 16; 17; 20; 21; 24; 25; 28; 30; 32; 34; 35; 40; 42; 48; 49; 50; 51; 56; 60; 68; 70; 75; 80; 84; 85; 96; 98; 100; 102; 105; 112; 119; 120; 136; 140; 147; 150; 160; 168; 170; 175; 196; 200; 204; 210; 224; 238; 240; 245; 255; 272; 280; 294; 300; 336; 340; 350; 357; 392; 400; 408; 420; 425; 476; 480; 490; 510; 525; 544; 560; 588; 595; 600; 672; 680; 700; 714; 735; 784; 800; 816; 833; 840; 850; 952; 980; 1,020; 1,050; 1,120; 1,176; 1,190; 1,200; 1,225; 1,275; 1,360; 1,400; 1,428; 1,470; 1,568; 1,632; 1,666; 1,680; 1,700; 1,785; 1,904; 1,960; 2,040; 2,100; 2,352; 2,380; 2,400; 2,450; 2,499; 2,550; 2,720; 2,800; 2,856; 2,940; 2,975; 3,332; 3,360; 3,400; 3,570; 3,675; 3,808; 3,920; 4,080; 4,165; 4,200; 4,704; 4,760; 4,900; 4,998; 5,100; 5,600; 5,712; 5,880; 5,950; 6,664; 6,800; 7,140; 7,350; 7,840; 8,160; 8,330; 8,400; 8,925; 9,520; 9,800; 9,996; 10,200; 11,424; 11,760; 11,900; 12,495; 13,328; 13,600; 14,280; 14,700; 16,660; 16,800; 17,850; 19,040; 19,600; 19,992; 20,400; 20,825; 23,520; 23,800; 24,990; 26,656; 28,560; 29,400; 33,320; 35,700; 39,200; 39,984; 40,800; 41,650; 47,600; 49,980; 57,120; 58,800; 62,475; 66,640; 71,400; 79,968; 83,300; 95,200; 99,960; 117,600; 124,950; 133,280; 142,800; 166,600; 199,920; 249,900; 285,600; 333,200; 399,840; 499,800; 666,400; 999,600 and 1,999,200
out of which 5 prime factors: 2; 3; 5; 7 and 17
1,999,200 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 1,999,199?

» What are all the proper, improper and prime factors (divisors) of the number 1,999,203?


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".