Given the Number 67,364,352, Calculate (Find) All the Factors (All the Divisors) of the Number 67,364,352 (the Proper, the Improper and the Prime Factors)

All the factors (divisors) of the number 67,364,352

1. Carry out the prime factorization of the number 67,364,352:

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

67,364,352 = 29 × 33 × 11 × 443
67,364,352 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 67,364,352

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
2 × 3 = 6
23 = 8
32 = 9
prime factor = 11
22 × 3 = 12
24 = 16
2 × 32 = 18
2 × 11 = 22
23 × 3 = 24
33 = 27
25 = 32
3 × 11 = 33
22 × 32 = 36
22 × 11 = 44
24 × 3 = 48
2 × 33 = 54
26 = 64
2 × 3 × 11 = 66
23 × 32 = 72
23 × 11 = 88
25 × 3 = 96
32 × 11 = 99
22 × 33 = 108
27 = 128
22 × 3 × 11 = 132
24 × 32 = 144
24 × 11 = 176
26 × 3 = 192
2 × 32 × 11 = 198
23 × 33 = 216
28 = 256
23 × 3 × 11 = 264
25 × 32 = 288
33 × 11 = 297
25 × 11 = 352
27 × 3 = 384
22 × 32 × 11 = 396
24 × 33 = 432
prime factor = 443
29 = 512
24 × 3 × 11 = 528
26 × 32 = 576
2 × 33 × 11 = 594
26 × 11 = 704
28 × 3 = 768
23 × 32 × 11 = 792
25 × 33 = 864
2 × 443 = 886
25 × 3 × 11 = 1,056
27 × 32 = 1,152
22 × 33 × 11 = 1,188
3 × 443 = 1,329
27 × 11 = 1,408
29 × 3 = 1,536
24 × 32 × 11 = 1,584
26 × 33 = 1,728
22 × 443 = 1,772
26 × 3 × 11 = 2,112
28 × 32 = 2,304
23 × 33 × 11 = 2,376
2 × 3 × 443 = 2,658
28 × 11 = 2,816
25 × 32 × 11 = 3,168
27 × 33 = 3,456
23 × 443 = 3,544
32 × 443 = 3,987
27 × 3 × 11 = 4,224
29 × 32 = 4,608
24 × 33 × 11 = 4,752
11 × 443 = 4,873
22 × 3 × 443 = 5,316
29 × 11 = 5,632
26 × 32 × 11 = 6,336
28 × 33 = 6,912
24 × 443 = 7,088
2 × 32 × 443 = 7,974
This list continues below...

... This list continues from above
28 × 3 × 11 = 8,448
25 × 33 × 11 = 9,504
2 × 11 × 443 = 9,746
23 × 3 × 443 = 10,632
33 × 443 = 11,961
27 × 32 × 11 = 12,672
29 × 33 = 13,824
25 × 443 = 14,176
3 × 11 × 443 = 14,619
22 × 32 × 443 = 15,948
29 × 3 × 11 = 16,896
26 × 33 × 11 = 19,008
22 × 11 × 443 = 19,492
24 × 3 × 443 = 21,264
2 × 33 × 443 = 23,922
28 × 32 × 11 = 25,344
26 × 443 = 28,352
2 × 3 × 11 × 443 = 29,238
23 × 32 × 443 = 31,896
27 × 33 × 11 = 38,016
23 × 11 × 443 = 38,984
25 × 3 × 443 = 42,528
32 × 11 × 443 = 43,857
22 × 33 × 443 = 47,844
29 × 32 × 11 = 50,688
27 × 443 = 56,704
22 × 3 × 11 × 443 = 58,476
24 × 32 × 443 = 63,792
28 × 33 × 11 = 76,032
24 × 11 × 443 = 77,968
26 × 3 × 443 = 85,056
2 × 32 × 11 × 443 = 87,714
23 × 33 × 443 = 95,688
28 × 443 = 113,408
23 × 3 × 11 × 443 = 116,952
25 × 32 × 443 = 127,584
33 × 11 × 443 = 131,571
29 × 33 × 11 = 152,064
25 × 11 × 443 = 155,936
27 × 3 × 443 = 170,112
22 × 32 × 11 × 443 = 175,428
24 × 33 × 443 = 191,376
29 × 443 = 226,816
24 × 3 × 11 × 443 = 233,904
26 × 32 × 443 = 255,168
2 × 33 × 11 × 443 = 263,142
26 × 11 × 443 = 311,872
28 × 3 × 443 = 340,224
23 × 32 × 11 × 443 = 350,856
25 × 33 × 443 = 382,752
25 × 3 × 11 × 443 = 467,808
27 × 32 × 443 = 510,336
22 × 33 × 11 × 443 = 526,284
27 × 11 × 443 = 623,744
29 × 3 × 443 = 680,448
24 × 32 × 11 × 443 = 701,712
26 × 33 × 443 = 765,504
26 × 3 × 11 × 443 = 935,616
28 × 32 × 443 = 1,020,672
23 × 33 × 11 × 443 = 1,052,568
28 × 11 × 443 = 1,247,488
25 × 32 × 11 × 443 = 1,403,424
27 × 33 × 443 = 1,531,008
27 × 3 × 11 × 443 = 1,871,232
29 × 32 × 443 = 2,041,344
24 × 33 × 11 × 443 = 2,105,136
29 × 11 × 443 = 2,494,976
26 × 32 × 11 × 443 = 2,806,848
28 × 33 × 443 = 3,062,016
28 × 3 × 11 × 443 = 3,742,464
25 × 33 × 11 × 443 = 4,210,272
27 × 32 × 11 × 443 = 5,613,696
29 × 33 × 443 = 6,124,032
29 × 3 × 11 × 443 = 7,484,928
26 × 33 × 11 × 443 = 8,420,544
28 × 32 × 11 × 443 = 11,227,392
27 × 33 × 11 × 443 = 16,841,088
29 × 32 × 11 × 443 = 22,454,784
28 × 33 × 11 × 443 = 33,682,176
29 × 33 × 11 × 443 = 67,364,352

The final answer:
(scroll down)

67,364,352 has 160 factors (divisors):
1; 2; 3; 4; 6; 8; 9; 11; 12; 16; 18; 22; 24; 27; 32; 33; 36; 44; 48; 54; 64; 66; 72; 88; 96; 99; 108; 128; 132; 144; 176; 192; 198; 216; 256; 264; 288; 297; 352; 384; 396; 432; 443; 512; 528; 576; 594; 704; 768; 792; 864; 886; 1,056; 1,152; 1,188; 1,329; 1,408; 1,536; 1,584; 1,728; 1,772; 2,112; 2,304; 2,376; 2,658; 2,816; 3,168; 3,456; 3,544; 3,987; 4,224; 4,608; 4,752; 4,873; 5,316; 5,632; 6,336; 6,912; 7,088; 7,974; 8,448; 9,504; 9,746; 10,632; 11,961; 12,672; 13,824; 14,176; 14,619; 15,948; 16,896; 19,008; 19,492; 21,264; 23,922; 25,344; 28,352; 29,238; 31,896; 38,016; 38,984; 42,528; 43,857; 47,844; 50,688; 56,704; 58,476; 63,792; 76,032; 77,968; 85,056; 87,714; 95,688; 113,408; 116,952; 127,584; 131,571; 152,064; 155,936; 170,112; 175,428; 191,376; 226,816; 233,904; 255,168; 263,142; 311,872; 340,224; 350,856; 382,752; 467,808; 510,336; 526,284; 623,744; 680,448; 701,712; 765,504; 935,616; 1,020,672; 1,052,568; 1,247,488; 1,403,424; 1,531,008; 1,871,232; 2,041,344; 2,105,136; 2,494,976; 2,806,848; 3,062,016; 3,742,464; 4,210,272; 5,613,696; 6,124,032; 7,484,928; 8,420,544; 11,227,392; 16,841,088; 22,454,784; 33,682,176 and 67,364,352
out of which 4 prime factors: 2; 3; 11 and 443
67,364,352 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 67,364,351?

» What are all the proper, improper and prime factors (divisors) of the number 67,364,354?


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".