Given the Number 142,767,360 Calculate (Find) All Its Factors (Divisors – the Proper, the Improper and the Prime Factors). Online Calculator

All the factors (divisors) of the number 142,767,360

1. Carry out the prime factorization of the number 142,767,360:

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


142,767,360 = 28 × 38 × 5 × 17
142,767,360 is not a prime number but a composite one.


* 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 142,767,360

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
23 = 8
32 = 9
2 × 5 = 10
22 × 3 = 12
3 × 5 = 15
24 = 16
prime factor = 17
2 × 32 = 18
22 × 5 = 20
23 × 3 = 24
33 = 27
2 × 3 × 5 = 30
25 = 32
2 × 17 = 34
22 × 32 = 36
23 × 5 = 40
32 × 5 = 45
24 × 3 = 48
3 × 17 = 51
2 × 33 = 54
22 × 3 × 5 = 60
26 = 64
22 × 17 = 68
23 × 32 = 72
24 × 5 = 80
34 = 81
5 × 17 = 85
2 × 32 × 5 = 90
25 × 3 = 96
2 × 3 × 17 = 102
22 × 33 = 108
23 × 3 × 5 = 120
27 = 128
33 × 5 = 135
23 × 17 = 136
24 × 32 = 144
32 × 17 = 153
25 × 5 = 160
2 × 34 = 162
2 × 5 × 17 = 170
22 × 32 × 5 = 180
26 × 3 = 192
22 × 3 × 17 = 204
23 × 33 = 216
24 × 3 × 5 = 240
35 = 243
3 × 5 × 17 = 255
28 = 256
2 × 33 × 5 = 270
24 × 17 = 272
25 × 32 = 288
2 × 32 × 17 = 306
26 × 5 = 320
22 × 34 = 324
22 × 5 × 17 = 340
23 × 32 × 5 = 360
27 × 3 = 384
34 × 5 = 405
23 × 3 × 17 = 408
24 × 33 = 432
33 × 17 = 459
25 × 3 × 5 = 480
2 × 35 = 486
2 × 3 × 5 × 17 = 510
22 × 33 × 5 = 540
25 × 17 = 544
26 × 32 = 576
22 × 32 × 17 = 612
27 × 5 = 640
23 × 34 = 648
23 × 5 × 17 = 680
24 × 32 × 5 = 720
36 = 729
32 × 5 × 17 = 765
28 × 3 = 768
2 × 34 × 5 = 810
24 × 3 × 17 = 816
25 × 33 = 864
2 × 33 × 17 = 918
26 × 3 × 5 = 960
22 × 35 = 972
22 × 3 × 5 × 17 = 1,020
23 × 33 × 5 = 1,080
26 × 17 = 1,088
27 × 32 = 1,152
35 × 5 = 1,215
23 × 32 × 17 = 1,224
28 × 5 = 1,280
24 × 34 = 1,296
24 × 5 × 17 = 1,360
34 × 17 = 1,377
25 × 32 × 5 = 1,440
2 × 36 = 1,458
2 × 32 × 5 × 17 = 1,530
22 × 34 × 5 = 1,620
25 × 3 × 17 = 1,632
26 × 33 = 1,728
22 × 33 × 17 = 1,836
27 × 3 × 5 = 1,920
23 × 35 = 1,944
23 × 3 × 5 × 17 = 2,040
24 × 33 × 5 = 2,160
27 × 17 = 2,176
37 = 2,187
33 × 5 × 17 = 2,295
28 × 32 = 2,304
2 × 35 × 5 = 2,430
24 × 32 × 17 = 2,448
25 × 34 = 2,592
25 × 5 × 17 = 2,720
2 × 34 × 17 = 2,754
26 × 32 × 5 = 2,880
22 × 36 = 2,916
22 × 32 × 5 × 17 = 3,060
23 × 34 × 5 = 3,240
26 × 3 × 17 = 3,264
27 × 33 = 3,456
36 × 5 = 3,645
23 × 33 × 17 = 3,672
28 × 3 × 5 = 3,840
24 × 35 = 3,888
24 × 3 × 5 × 17 = 4,080
35 × 17 = 4,131
25 × 33 × 5 = 4,320
28 × 17 = 4,352
2 × 37 = 4,374
2 × 33 × 5 × 17 = 4,590
22 × 35 × 5 = 4,860
25 × 32 × 17 = 4,896
26 × 34 = 5,184
26 × 5 × 17 = 5,440
22 × 34 × 17 = 5,508
27 × 32 × 5 = 5,760
23 × 36 = 5,832
23 × 32 × 5 × 17 = 6,120
24 × 34 × 5 = 6,480
27 × 3 × 17 = 6,528
38 = 6,561
34 × 5 × 17 = 6,885
28 × 33 = 6,912
2 × 36 × 5 = 7,290
24 × 33 × 17 = 7,344
25 × 35 = 7,776
25 × 3 × 5 × 17 = 8,160
2 × 35 × 17 = 8,262
26 × 33 × 5 = 8,640
22 × 37 = 8,748
22 × 33 × 5 × 17 = 9,180
23 × 35 × 5 = 9,720
26 × 32 × 17 = 9,792
27 × 34 = 10,368
27 × 5 × 17 = 10,880
37 × 5 = 10,935
23 × 34 × 17 = 11,016
28 × 32 × 5 = 11,520
24 × 36 = 11,664
This list continues below...

... This list continues from above
24 × 32 × 5 × 17 = 12,240
36 × 17 = 12,393
25 × 34 × 5 = 12,960
28 × 3 × 17 = 13,056
2 × 38 = 13,122
2 × 34 × 5 × 17 = 13,770
22 × 36 × 5 = 14,580
25 × 33 × 17 = 14,688
26 × 35 = 15,552
26 × 3 × 5 × 17 = 16,320
22 × 35 × 17 = 16,524
27 × 33 × 5 = 17,280
23 × 37 = 17,496
23 × 33 × 5 × 17 = 18,360
24 × 35 × 5 = 19,440
27 × 32 × 17 = 19,584
35 × 5 × 17 = 20,655
28 × 34 = 20,736
28 × 5 × 17 = 21,760
2 × 37 × 5 = 21,870
24 × 34 × 17 = 22,032
25 × 36 = 23,328
25 × 32 × 5 × 17 = 24,480
2 × 36 × 17 = 24,786
26 × 34 × 5 = 25,920
22 × 38 = 26,244
22 × 34 × 5 × 17 = 27,540
23 × 36 × 5 = 29,160
26 × 33 × 17 = 29,376
27 × 35 = 31,104
27 × 3 × 5 × 17 = 32,640
38 × 5 = 32,805
23 × 35 × 17 = 33,048
28 × 33 × 5 = 34,560
24 × 37 = 34,992
24 × 33 × 5 × 17 = 36,720
37 × 17 = 37,179
25 × 35 × 5 = 38,880
28 × 32 × 17 = 39,168
2 × 35 × 5 × 17 = 41,310
22 × 37 × 5 = 43,740
25 × 34 × 17 = 44,064
26 × 36 = 46,656
26 × 32 × 5 × 17 = 48,960
22 × 36 × 17 = 49,572
27 × 34 × 5 = 51,840
23 × 38 = 52,488
23 × 34 × 5 × 17 = 55,080
24 × 36 × 5 = 58,320
27 × 33 × 17 = 58,752
36 × 5 × 17 = 61,965
28 × 35 = 62,208
28 × 3 × 5 × 17 = 65,280
2 × 38 × 5 = 65,610
24 × 35 × 17 = 66,096
25 × 37 = 69,984
25 × 33 × 5 × 17 = 73,440
2 × 37 × 17 = 74,358
26 × 35 × 5 = 77,760
22 × 35 × 5 × 17 = 82,620
23 × 37 × 5 = 87,480
26 × 34 × 17 = 88,128
27 × 36 = 93,312
27 × 32 × 5 × 17 = 97,920
23 × 36 × 17 = 99,144
28 × 34 × 5 = 103,680
24 × 38 = 104,976
24 × 34 × 5 × 17 = 110,160
38 × 17 = 111,537
25 × 36 × 5 = 116,640
28 × 33 × 17 = 117,504
2 × 36 × 5 × 17 = 123,930
22 × 38 × 5 = 131,220
25 × 35 × 17 = 132,192
26 × 37 = 139,968
26 × 33 × 5 × 17 = 146,880
22 × 37 × 17 = 148,716
27 × 35 × 5 = 155,520
23 × 35 × 5 × 17 = 165,240
24 × 37 × 5 = 174,960
27 × 34 × 17 = 176,256
37 × 5 × 17 = 185,895
28 × 36 = 186,624
28 × 32 × 5 × 17 = 195,840
24 × 36 × 17 = 198,288
25 × 38 = 209,952
25 × 34 × 5 × 17 = 220,320
2 × 38 × 17 = 223,074
26 × 36 × 5 = 233,280
22 × 36 × 5 × 17 = 247,860
23 × 38 × 5 = 262,440
26 × 35 × 17 = 264,384
27 × 37 = 279,936
27 × 33 × 5 × 17 = 293,760
23 × 37 × 17 = 297,432
28 × 35 × 5 = 311,040
24 × 35 × 5 × 17 = 330,480
25 × 37 × 5 = 349,920
28 × 34 × 17 = 352,512
2 × 37 × 5 × 17 = 371,790
25 × 36 × 17 = 396,576
26 × 38 = 419,904
26 × 34 × 5 × 17 = 440,640
22 × 38 × 17 = 446,148
27 × 36 × 5 = 466,560
23 × 36 × 5 × 17 = 495,720
24 × 38 × 5 = 524,880
27 × 35 × 17 = 528,768
38 × 5 × 17 = 557,685
28 × 37 = 559,872
28 × 33 × 5 × 17 = 587,520
24 × 37 × 17 = 594,864
25 × 35 × 5 × 17 = 660,960
26 × 37 × 5 = 699,840
22 × 37 × 5 × 17 = 743,580
26 × 36 × 17 = 793,152
27 × 38 = 839,808
27 × 34 × 5 × 17 = 881,280
23 × 38 × 17 = 892,296
28 × 36 × 5 = 933,120
24 × 36 × 5 × 17 = 991,440
25 × 38 × 5 = 1,049,760
28 × 35 × 17 = 1,057,536
2 × 38 × 5 × 17 = 1,115,370
25 × 37 × 17 = 1,189,728
26 × 35 × 5 × 17 = 1,321,920
27 × 37 × 5 = 1,399,680
23 × 37 × 5 × 17 = 1,487,160
27 × 36 × 17 = 1,586,304
28 × 38 = 1,679,616
28 × 34 × 5 × 17 = 1,762,560
24 × 38 × 17 = 1,784,592
25 × 36 × 5 × 17 = 1,982,880
26 × 38 × 5 = 2,099,520
22 × 38 × 5 × 17 = 2,230,740
26 × 37 × 17 = 2,379,456
27 × 35 × 5 × 17 = 2,643,840
28 × 37 × 5 = 2,799,360
24 × 37 × 5 × 17 = 2,974,320
28 × 36 × 17 = 3,172,608
25 × 38 × 17 = 3,569,184
26 × 36 × 5 × 17 = 3,965,760
27 × 38 × 5 = 4,199,040
23 × 38 × 5 × 17 = 4,461,480
27 × 37 × 17 = 4,758,912
28 × 35 × 5 × 17 = 5,287,680
25 × 37 × 5 × 17 = 5,948,640
26 × 38 × 17 = 7,138,368
27 × 36 × 5 × 17 = 7,931,520
28 × 38 × 5 = 8,398,080
24 × 38 × 5 × 17 = 8,922,960
28 × 37 × 17 = 9,517,824
26 × 37 × 5 × 17 = 11,897,280
27 × 38 × 17 = 14,276,736
28 × 36 × 5 × 17 = 15,863,040
25 × 38 × 5 × 17 = 17,845,920
27 × 37 × 5 × 17 = 23,794,560
28 × 38 × 17 = 28,553,472
26 × 38 × 5 × 17 = 35,691,840
28 × 37 × 5 × 17 = 47,589,120
27 × 38 × 5 × 17 = 71,383,680
28 × 38 × 5 × 17 = 142,767,360

The final answer:
(scroll down)

142,767,360 has 324 factors (divisors):
1; 2; 3; 4; 5; 6; 8; 9; 10; 12; 15; 16; 17; 18; 20; 24; 27; 30; 32; 34; 36; 40; 45; 48; 51; 54; 60; 64; 68; 72; 80; 81; 85; 90; 96; 102; 108; 120; 128; 135; 136; 144; 153; 160; 162; 170; 180; 192; 204; 216; 240; 243; 255; 256; 270; 272; 288; 306; 320; 324; 340; 360; 384; 405; 408; 432; 459; 480; 486; 510; 540; 544; 576; 612; 640; 648; 680; 720; 729; 765; 768; 810; 816; 864; 918; 960; 972; 1,020; 1,080; 1,088; 1,152; 1,215; 1,224; 1,280; 1,296; 1,360; 1,377; 1,440; 1,458; 1,530; 1,620; 1,632; 1,728; 1,836; 1,920; 1,944; 2,040; 2,160; 2,176; 2,187; 2,295; 2,304; 2,430; 2,448; 2,592; 2,720; 2,754; 2,880; 2,916; 3,060; 3,240; 3,264; 3,456; 3,645; 3,672; 3,840; 3,888; 4,080; 4,131; 4,320; 4,352; 4,374; 4,590; 4,860; 4,896; 5,184; 5,440; 5,508; 5,760; 5,832; 6,120; 6,480; 6,528; 6,561; 6,885; 6,912; 7,290; 7,344; 7,776; 8,160; 8,262; 8,640; 8,748; 9,180; 9,720; 9,792; 10,368; 10,880; 10,935; 11,016; 11,520; 11,664; 12,240; 12,393; 12,960; 13,056; 13,122; 13,770; 14,580; 14,688; 15,552; 16,320; 16,524; 17,280; 17,496; 18,360; 19,440; 19,584; 20,655; 20,736; 21,760; 21,870; 22,032; 23,328; 24,480; 24,786; 25,920; 26,244; 27,540; 29,160; 29,376; 31,104; 32,640; 32,805; 33,048; 34,560; 34,992; 36,720; 37,179; 38,880; 39,168; 41,310; 43,740; 44,064; 46,656; 48,960; 49,572; 51,840; 52,488; 55,080; 58,320; 58,752; 61,965; 62,208; 65,280; 65,610; 66,096; 69,984; 73,440; 74,358; 77,760; 82,620; 87,480; 88,128; 93,312; 97,920; 99,144; 103,680; 104,976; 110,160; 111,537; 116,640; 117,504; 123,930; 131,220; 132,192; 139,968; 146,880; 148,716; 155,520; 165,240; 174,960; 176,256; 185,895; 186,624; 195,840; 198,288; 209,952; 220,320; 223,074; 233,280; 247,860; 262,440; 264,384; 279,936; 293,760; 297,432; 311,040; 330,480; 349,920; 352,512; 371,790; 396,576; 419,904; 440,640; 446,148; 466,560; 495,720; 524,880; 528,768; 557,685; 559,872; 587,520; 594,864; 660,960; 699,840; 743,580; 793,152; 839,808; 881,280; 892,296; 933,120; 991,440; 1,049,760; 1,057,536; 1,115,370; 1,189,728; 1,321,920; 1,399,680; 1,487,160; 1,586,304; 1,679,616; 1,762,560; 1,784,592; 1,982,880; 2,099,520; 2,230,740; 2,379,456; 2,643,840; 2,799,360; 2,974,320; 3,172,608; 3,569,184; 3,965,760; 4,199,040; 4,461,480; 4,758,912; 5,287,680; 5,948,640; 7,138,368; 7,931,520; 8,398,080; 8,922,960; 9,517,824; 11,897,280; 14,276,736; 15,863,040; 17,845,920; 23,794,560; 28,553,472; 35,691,840; 47,589,120; 71,383,680 and 142,767,360
out of which 4 prime factors: 2; 3; 5 and 17
142,767,360 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.


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".