Given the Number 1,722,240, Calculate (Find) All the Factors (All the Divisors) of the Number 1,722,240 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 1,722,240

1. Carry out the prime factorization of the number 1,722,240:

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

1,722,240 = 27 × 32 × 5 × 13 × 23
1,722,240 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 1,722,240

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
32 = 9
2 × 5 = 10
22 × 3 = 12
prime factor = 13
3 × 5 = 15
24 = 16
2 × 32 = 18
22 × 5 = 20
prime factor = 23
23 × 3 = 24
2 × 13 = 26
2 × 3 × 5 = 30
25 = 32
22 × 32 = 36
3 × 13 = 39
23 × 5 = 40
32 × 5 = 45
2 × 23 = 46
24 × 3 = 48
22 × 13 = 52
22 × 3 × 5 = 60
26 = 64
5 × 13 = 65
3 × 23 = 69
23 × 32 = 72
2 × 3 × 13 = 78
24 × 5 = 80
2 × 32 × 5 = 90
22 × 23 = 92
25 × 3 = 96
23 × 13 = 104
5 × 23 = 115
32 × 13 = 117
23 × 3 × 5 = 120
27 = 128
2 × 5 × 13 = 130
2 × 3 × 23 = 138
24 × 32 = 144
22 × 3 × 13 = 156
25 × 5 = 160
22 × 32 × 5 = 180
23 × 23 = 184
26 × 3 = 192
3 × 5 × 13 = 195
32 × 23 = 207
24 × 13 = 208
2 × 5 × 23 = 230
2 × 32 × 13 = 234
24 × 3 × 5 = 240
22 × 5 × 13 = 260
22 × 3 × 23 = 276
25 × 32 = 288
13 × 23 = 299
23 × 3 × 13 = 312
26 × 5 = 320
3 × 5 × 23 = 345
23 × 32 × 5 = 360
24 × 23 = 368
27 × 3 = 384
2 × 3 × 5 × 13 = 390
2 × 32 × 23 = 414
25 × 13 = 416
22 × 5 × 23 = 460
22 × 32 × 13 = 468
25 × 3 × 5 = 480
23 × 5 × 13 = 520
23 × 3 × 23 = 552
26 × 32 = 576
32 × 5 × 13 = 585
2 × 13 × 23 = 598
24 × 3 × 13 = 624
27 × 5 = 640
2 × 3 × 5 × 23 = 690
24 × 32 × 5 = 720
25 × 23 = 736
22 × 3 × 5 × 13 = 780
22 × 32 × 23 = 828
26 × 13 = 832
3 × 13 × 23 = 897
23 × 5 × 23 = 920
23 × 32 × 13 = 936
26 × 3 × 5 = 960
32 × 5 × 23 = 1,035
24 × 5 × 13 = 1,040
24 × 3 × 23 = 1,104
27 × 32 = 1,152
2 × 32 × 5 × 13 = 1,170
22 × 13 × 23 = 1,196
25 × 3 × 13 = 1,248
This list continues below...

... This list continues from above
22 × 3 × 5 × 23 = 1,380
25 × 32 × 5 = 1,440
26 × 23 = 1,472
5 × 13 × 23 = 1,495
23 × 3 × 5 × 13 = 1,560
23 × 32 × 23 = 1,656
27 × 13 = 1,664
2 × 3 × 13 × 23 = 1,794
24 × 5 × 23 = 1,840
24 × 32 × 13 = 1,872
27 × 3 × 5 = 1,920
2 × 32 × 5 × 23 = 2,070
25 × 5 × 13 = 2,080
25 × 3 × 23 = 2,208
22 × 32 × 5 × 13 = 2,340
23 × 13 × 23 = 2,392
26 × 3 × 13 = 2,496
32 × 13 × 23 = 2,691
23 × 3 × 5 × 23 = 2,760
26 × 32 × 5 = 2,880
27 × 23 = 2,944
2 × 5 × 13 × 23 = 2,990
24 × 3 × 5 × 13 = 3,120
24 × 32 × 23 = 3,312
22 × 3 × 13 × 23 = 3,588
25 × 5 × 23 = 3,680
25 × 32 × 13 = 3,744
22 × 32 × 5 × 23 = 4,140
26 × 5 × 13 = 4,160
26 × 3 × 23 = 4,416
3 × 5 × 13 × 23 = 4,485
23 × 32 × 5 × 13 = 4,680
24 × 13 × 23 = 4,784
27 × 3 × 13 = 4,992
2 × 32 × 13 × 23 = 5,382
24 × 3 × 5 × 23 = 5,520
27 × 32 × 5 = 5,760
22 × 5 × 13 × 23 = 5,980
25 × 3 × 5 × 13 = 6,240
25 × 32 × 23 = 6,624
23 × 3 × 13 × 23 = 7,176
26 × 5 × 23 = 7,360
26 × 32 × 13 = 7,488
23 × 32 × 5 × 23 = 8,280
27 × 5 × 13 = 8,320
27 × 3 × 23 = 8,832
2 × 3 × 5 × 13 × 23 = 8,970
24 × 32 × 5 × 13 = 9,360
25 × 13 × 23 = 9,568
22 × 32 × 13 × 23 = 10,764
25 × 3 × 5 × 23 = 11,040
23 × 5 × 13 × 23 = 11,960
26 × 3 × 5 × 13 = 12,480
26 × 32 × 23 = 13,248
32 × 5 × 13 × 23 = 13,455
24 × 3 × 13 × 23 = 14,352
27 × 5 × 23 = 14,720
27 × 32 × 13 = 14,976
24 × 32 × 5 × 23 = 16,560
22 × 3 × 5 × 13 × 23 = 17,940
25 × 32 × 5 × 13 = 18,720
26 × 13 × 23 = 19,136
23 × 32 × 13 × 23 = 21,528
26 × 3 × 5 × 23 = 22,080
24 × 5 × 13 × 23 = 23,920
27 × 3 × 5 × 13 = 24,960
27 × 32 × 23 = 26,496
2 × 32 × 5 × 13 × 23 = 26,910
25 × 3 × 13 × 23 = 28,704
25 × 32 × 5 × 23 = 33,120
23 × 3 × 5 × 13 × 23 = 35,880
26 × 32 × 5 × 13 = 37,440
27 × 13 × 23 = 38,272
24 × 32 × 13 × 23 = 43,056
27 × 3 × 5 × 23 = 44,160
25 × 5 × 13 × 23 = 47,840
22 × 32 × 5 × 13 × 23 = 53,820
26 × 3 × 13 × 23 = 57,408
26 × 32 × 5 × 23 = 66,240
24 × 3 × 5 × 13 × 23 = 71,760
27 × 32 × 5 × 13 = 74,880
25 × 32 × 13 × 23 = 86,112
26 × 5 × 13 × 23 = 95,680
23 × 32 × 5 × 13 × 23 = 107,640
27 × 3 × 13 × 23 = 114,816
27 × 32 × 5 × 23 = 132,480
25 × 3 × 5 × 13 × 23 = 143,520
26 × 32 × 13 × 23 = 172,224
27 × 5 × 13 × 23 = 191,360
24 × 32 × 5 × 13 × 23 = 215,280
26 × 3 × 5 × 13 × 23 = 287,040
27 × 32 × 13 × 23 = 344,448
25 × 32 × 5 × 13 × 23 = 430,560
27 × 3 × 5 × 13 × 23 = 574,080
26 × 32 × 5 × 13 × 23 = 861,120
27 × 32 × 5 × 13 × 23 = 1,722,240

The final answer:
(scroll down)

1,722,240 has 192 factors (divisors):
1; 2; 3; 4; 5; 6; 8; 9; 10; 12; 13; 15; 16; 18; 20; 23; 24; 26; 30; 32; 36; 39; 40; 45; 46; 48; 52; 60; 64; 65; 69; 72; 78; 80; 90; 92; 96; 104; 115; 117; 120; 128; 130; 138; 144; 156; 160; 180; 184; 192; 195; 207; 208; 230; 234; 240; 260; 276; 288; 299; 312; 320; 345; 360; 368; 384; 390; 414; 416; 460; 468; 480; 520; 552; 576; 585; 598; 624; 640; 690; 720; 736; 780; 828; 832; 897; 920; 936; 960; 1,035; 1,040; 1,104; 1,152; 1,170; 1,196; 1,248; 1,380; 1,440; 1,472; 1,495; 1,560; 1,656; 1,664; 1,794; 1,840; 1,872; 1,920; 2,070; 2,080; 2,208; 2,340; 2,392; 2,496; 2,691; 2,760; 2,880; 2,944; 2,990; 3,120; 3,312; 3,588; 3,680; 3,744; 4,140; 4,160; 4,416; 4,485; 4,680; 4,784; 4,992; 5,382; 5,520; 5,760; 5,980; 6,240; 6,624; 7,176; 7,360; 7,488; 8,280; 8,320; 8,832; 8,970; 9,360; 9,568; 10,764; 11,040; 11,960; 12,480; 13,248; 13,455; 14,352; 14,720; 14,976; 16,560; 17,940; 18,720; 19,136; 21,528; 22,080; 23,920; 24,960; 26,496; 26,910; 28,704; 33,120; 35,880; 37,440; 38,272; 43,056; 44,160; 47,840; 53,820; 57,408; 66,240; 71,760; 74,880; 86,112; 95,680; 107,640; 114,816; 132,480; 143,520; 172,224; 191,360; 215,280; 287,040; 344,448; 430,560; 574,080; 861,120 and 1,722,240
out of which 5 prime factors: 2; 3; 5; 13 and 23
1,722,240 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 1,722,228?

» What are all the proper, improper and prime factors (divisors) of the number 1,722,254?


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".