Given the Number 1,746,360, Calculate (Find) All the Factors (All the Divisors) of the Number 1,746,360 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 1,746,360

1. Carry out the prime factorization of the number 1,746,360:

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

1,746,360 = 23 × 34 × 5 × 72 × 11
1,746,360 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 1,746,360

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
32 = 9
2 × 5 = 10
prime factor = 11
22 × 3 = 12
2 × 7 = 14
3 × 5 = 15
2 × 32 = 18
22 × 5 = 20
3 × 7 = 21
2 × 11 = 22
23 × 3 = 24
33 = 27
22 × 7 = 28
2 × 3 × 5 = 30
3 × 11 = 33
5 × 7 = 35
22 × 32 = 36
23 × 5 = 40
2 × 3 × 7 = 42
22 × 11 = 44
32 × 5 = 45
72 = 49
2 × 33 = 54
5 × 11 = 55
23 × 7 = 56
22 × 3 × 5 = 60
32 × 7 = 63
2 × 3 × 11 = 66
2 × 5 × 7 = 70
23 × 32 = 72
7 × 11 = 77
34 = 81
22 × 3 × 7 = 84
23 × 11 = 88
2 × 32 × 5 = 90
2 × 72 = 98
32 × 11 = 99
3 × 5 × 7 = 105
22 × 33 = 108
2 × 5 × 11 = 110
23 × 3 × 5 = 120
2 × 32 × 7 = 126
22 × 3 × 11 = 132
33 × 5 = 135
22 × 5 × 7 = 140
3 × 72 = 147
2 × 7 × 11 = 154
2 × 34 = 162
3 × 5 × 11 = 165
23 × 3 × 7 = 168
22 × 32 × 5 = 180
33 × 7 = 189
22 × 72 = 196
2 × 32 × 11 = 198
2 × 3 × 5 × 7 = 210
23 × 33 = 216
22 × 5 × 11 = 220
3 × 7 × 11 = 231
5 × 72 = 245
22 × 32 × 7 = 252
23 × 3 × 11 = 264
2 × 33 × 5 = 270
23 × 5 × 7 = 280
2 × 3 × 72 = 294
33 × 11 = 297
22 × 7 × 11 = 308
32 × 5 × 7 = 315
22 × 34 = 324
2 × 3 × 5 × 11 = 330
23 × 32 × 5 = 360
2 × 33 × 7 = 378
5 × 7 × 11 = 385
23 × 72 = 392
22 × 32 × 11 = 396
34 × 5 = 405
22 × 3 × 5 × 7 = 420
23 × 5 × 11 = 440
32 × 72 = 441
2 × 3 × 7 × 11 = 462
2 × 5 × 72 = 490
32 × 5 × 11 = 495
23 × 32 × 7 = 504
72 × 11 = 539
22 × 33 × 5 = 540
34 × 7 = 567
22 × 3 × 72 = 588
2 × 33 × 11 = 594
23 × 7 × 11 = 616
2 × 32 × 5 × 7 = 630
23 × 34 = 648
22 × 3 × 5 × 11 = 660
32 × 7 × 11 = 693
3 × 5 × 72 = 735
22 × 33 × 7 = 756
2 × 5 × 7 × 11 = 770
23 × 32 × 11 = 792
2 × 34 × 5 = 810
23 × 3 × 5 × 7 = 840
2 × 32 × 72 = 882
34 × 11 = 891
22 × 3 × 7 × 11 = 924
33 × 5 × 7 = 945
22 × 5 × 72 = 980
2 × 32 × 5 × 11 = 990
2 × 72 × 11 = 1,078
23 × 33 × 5 = 1,080
2 × 34 × 7 = 1,134
3 × 5 × 7 × 11 = 1,155
23 × 3 × 72 = 1,176
22 × 33 × 11 = 1,188
22 × 32 × 5 × 7 = 1,260
23 × 3 × 5 × 11 = 1,320
This list continues below...

... This list continues from above
33 × 72 = 1,323
2 × 32 × 7 × 11 = 1,386
2 × 3 × 5 × 72 = 1,470
33 × 5 × 11 = 1,485
23 × 33 × 7 = 1,512
22 × 5 × 7 × 11 = 1,540
3 × 72 × 11 = 1,617
22 × 34 × 5 = 1,620
22 × 32 × 72 = 1,764
2 × 34 × 11 = 1,782
23 × 3 × 7 × 11 = 1,848
2 × 33 × 5 × 7 = 1,890
23 × 5 × 72 = 1,960
22 × 32 × 5 × 11 = 1,980
33 × 7 × 11 = 2,079
22 × 72 × 11 = 2,156
32 × 5 × 72 = 2,205
22 × 34 × 7 = 2,268
2 × 3 × 5 × 7 × 11 = 2,310
23 × 33 × 11 = 2,376
23 × 32 × 5 × 7 = 2,520
2 × 33 × 72 = 2,646
5 × 72 × 11 = 2,695
22 × 32 × 7 × 11 = 2,772
34 × 5 × 7 = 2,835
22 × 3 × 5 × 72 = 2,940
2 × 33 × 5 × 11 = 2,970
23 × 5 × 7 × 11 = 3,080
2 × 3 × 72 × 11 = 3,234
23 × 34 × 5 = 3,240
32 × 5 × 7 × 11 = 3,465
23 × 32 × 72 = 3,528
22 × 34 × 11 = 3,564
22 × 33 × 5 × 7 = 3,780
23 × 32 × 5 × 11 = 3,960
34 × 72 = 3,969
2 × 33 × 7 × 11 = 4,158
23 × 72 × 11 = 4,312
2 × 32 × 5 × 72 = 4,410
34 × 5 × 11 = 4,455
23 × 34 × 7 = 4,536
22 × 3 × 5 × 7 × 11 = 4,620
32 × 72 × 11 = 4,851
22 × 33 × 72 = 5,292
2 × 5 × 72 × 11 = 5,390
23 × 32 × 7 × 11 = 5,544
2 × 34 × 5 × 7 = 5,670
23 × 3 × 5 × 72 = 5,880
22 × 33 × 5 × 11 = 5,940
34 × 7 × 11 = 6,237
22 × 3 × 72 × 11 = 6,468
33 × 5 × 72 = 6,615
2 × 32 × 5 × 7 × 11 = 6,930
23 × 34 × 11 = 7,128
23 × 33 × 5 × 7 = 7,560
2 × 34 × 72 = 7,938
3 × 5 × 72 × 11 = 8,085
22 × 33 × 7 × 11 = 8,316
22 × 32 × 5 × 72 = 8,820
2 × 34 × 5 × 11 = 8,910
23 × 3 × 5 × 7 × 11 = 9,240
2 × 32 × 72 × 11 = 9,702
33 × 5 × 7 × 11 = 10,395
23 × 33 × 72 = 10,584
22 × 5 × 72 × 11 = 10,780
22 × 34 × 5 × 7 = 11,340
23 × 33 × 5 × 11 = 11,880
2 × 34 × 7 × 11 = 12,474
23 × 3 × 72 × 11 = 12,936
2 × 33 × 5 × 72 = 13,230
22 × 32 × 5 × 7 × 11 = 13,860
33 × 72 × 11 = 14,553
22 × 34 × 72 = 15,876
2 × 3 × 5 × 72 × 11 = 16,170
23 × 33 × 7 × 11 = 16,632
23 × 32 × 5 × 72 = 17,640
22 × 34 × 5 × 11 = 17,820
22 × 32 × 72 × 11 = 19,404
34 × 5 × 72 = 19,845
2 × 33 × 5 × 7 × 11 = 20,790
23 × 5 × 72 × 11 = 21,560
23 × 34 × 5 × 7 = 22,680
32 × 5 × 72 × 11 = 24,255
22 × 34 × 7 × 11 = 24,948
22 × 33 × 5 × 72 = 26,460
23 × 32 × 5 × 7 × 11 = 27,720
2 × 33 × 72 × 11 = 29,106
34 × 5 × 7 × 11 = 31,185
23 × 34 × 72 = 31,752
22 × 3 × 5 × 72 × 11 = 32,340
23 × 34 × 5 × 11 = 35,640
23 × 32 × 72 × 11 = 38,808
2 × 34 × 5 × 72 = 39,690
22 × 33 × 5 × 7 × 11 = 41,580
34 × 72 × 11 = 43,659
2 × 32 × 5 × 72 × 11 = 48,510
23 × 34 × 7 × 11 = 49,896
23 × 33 × 5 × 72 = 52,920
22 × 33 × 72 × 11 = 58,212
2 × 34 × 5 × 7 × 11 = 62,370
23 × 3 × 5 × 72 × 11 = 64,680
33 × 5 × 72 × 11 = 72,765
22 × 34 × 5 × 72 = 79,380
23 × 33 × 5 × 7 × 11 = 83,160
2 × 34 × 72 × 11 = 87,318
22 × 32 × 5 × 72 × 11 = 97,020
23 × 33 × 72 × 11 = 116,424
22 × 34 × 5 × 7 × 11 = 124,740
2 × 33 × 5 × 72 × 11 = 145,530
23 × 34 × 5 × 72 = 158,760
22 × 34 × 72 × 11 = 174,636
23 × 32 × 5 × 72 × 11 = 194,040
34 × 5 × 72 × 11 = 218,295
23 × 34 × 5 × 7 × 11 = 249,480
22 × 33 × 5 × 72 × 11 = 291,060
23 × 34 × 72 × 11 = 349,272
2 × 34 × 5 × 72 × 11 = 436,590
23 × 33 × 5 × 72 × 11 = 582,120
22 × 34 × 5 × 72 × 11 = 873,180
23 × 34 × 5 × 72 × 11 = 1,746,360

The final answer:
(scroll down)

1,746,360 has 240 factors (divisors):
1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 14; 15; 18; 20; 21; 22; 24; 27; 28; 30; 33; 35; 36; 40; 42; 44; 45; 49; 54; 55; 56; 60; 63; 66; 70; 72; 77; 81; 84; 88; 90; 98; 99; 105; 108; 110; 120; 126; 132; 135; 140; 147; 154; 162; 165; 168; 180; 189; 196; 198; 210; 216; 220; 231; 245; 252; 264; 270; 280; 294; 297; 308; 315; 324; 330; 360; 378; 385; 392; 396; 405; 420; 440; 441; 462; 490; 495; 504; 539; 540; 567; 588; 594; 616; 630; 648; 660; 693; 735; 756; 770; 792; 810; 840; 882; 891; 924; 945; 980; 990; 1,078; 1,080; 1,134; 1,155; 1,176; 1,188; 1,260; 1,320; 1,323; 1,386; 1,470; 1,485; 1,512; 1,540; 1,617; 1,620; 1,764; 1,782; 1,848; 1,890; 1,960; 1,980; 2,079; 2,156; 2,205; 2,268; 2,310; 2,376; 2,520; 2,646; 2,695; 2,772; 2,835; 2,940; 2,970; 3,080; 3,234; 3,240; 3,465; 3,528; 3,564; 3,780; 3,960; 3,969; 4,158; 4,312; 4,410; 4,455; 4,536; 4,620; 4,851; 5,292; 5,390; 5,544; 5,670; 5,880; 5,940; 6,237; 6,468; 6,615; 6,930; 7,128; 7,560; 7,938; 8,085; 8,316; 8,820; 8,910; 9,240; 9,702; 10,395; 10,584; 10,780; 11,340; 11,880; 12,474; 12,936; 13,230; 13,860; 14,553; 15,876; 16,170; 16,632; 17,640; 17,820; 19,404; 19,845; 20,790; 21,560; 22,680; 24,255; 24,948; 26,460; 27,720; 29,106; 31,185; 31,752; 32,340; 35,640; 38,808; 39,690; 41,580; 43,659; 48,510; 49,896; 52,920; 58,212; 62,370; 64,680; 72,765; 79,380; 83,160; 87,318; 97,020; 116,424; 124,740; 145,530; 158,760; 174,636; 194,040; 218,295; 249,480; 291,060; 349,272; 436,590; 582,120; 873,180 and 1,746,360
out of which 5 prime factors: 2; 3; 5; 7 and 11
1,746,360 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 1,746,346?

» What are all the proper, improper and prime factors (divisors) of the number 1,746,368?


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".