Factors of 349,272. Calculator of Proper, Improper, Prime and Compound Divisors, if Any

All the factors (divisors) of the number 349,272. Connection with the prime factorization of the number

To find all the divisors of the number 349,272:

  • 1. Decompose the number into prime factors.
  • See how you can find out how many factors (divisors) the number has, without actually calculating them.
  • 2. Multiply the prime factors in all their unique combinations, that yield different results.

1. Carry out the prime factorization of the number 349,272:

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


349,272 = 23 × 34 × 72 × 11
349,272 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.
  • Examples of prime numbers: 2 (factors 1, 2), 3 (factors 1, 3), 5 (factors 1, 5), 7 (factors 1, 7), 11 (factors 1, 11), 13 (factors 1, 13), ...
  • Composite number: a natural number that has at least one factor other than 1 and itself. So it is neither a prime number nor 1.
  • Examples of composite numbers: 4 (it has 3 factors: 1, 2, 4), 6 (it has 4 factors: 1, 2, 3, 6), 8 (it has 4 factors: 1, 2, 4, 8), 9 (it has 3 factors: 1, 3, 9), 10 (it has 4 factors: 1, 2, 5, 10), 12 (it has 6 factors: 1, 2, 3, 4, 6, 12), ...

  • » Online calculator. Check whether a number is prime or not. The prime factorization of composite numbers (decomposition into prime factors)


How to count the number of factors of a number?

Without actually finding the factors

  • If a number N is prime factorized as:
    N = am × bk × cz
    where a, b, c are the prime factors and m, k, z are their exponents, natural numbers, ....
  • ...
  • Then the number of factors of the number N can be calculated as:
    n = (m + 1) × (k + 1) × (z + 1)
  • ...
  • In our case, the number of factors is calculated as:
  • n = (3 + 1) × (4 + 1) × (2 + 1) × (1 + 1) = 4 × 5 × 3 × 2 = 120

But to actually calculate the factors, see below...

2. Multiply the prime factors of the number 349,272

  • 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):

Numbers other than 1 that are not prime factors are composite factors (divisors).

neither prime nor composite = 1
prime factor = 2
prime factor = 3
composite factor = 22 = 4
composite factor = 2 × 3 = 6
prime factor = 7
composite factor = 23 = 8
composite factor = 32 = 9
prime factor = 11
composite factor = 22 × 3 = 12
composite factor = 2 × 7 = 14
composite factor = 2 × 32 = 18
composite factor = 3 × 7 = 21
composite factor = 2 × 11 = 22
composite factor = 23 × 3 = 24
composite factor = 33 = 27
composite factor = 22 × 7 = 28
composite factor = 3 × 11 = 33
composite factor = 22 × 32 = 36
composite factor = 2 × 3 × 7 = 42
composite factor = 22 × 11 = 44
composite factor = 72 = 49
composite factor = 2 × 33 = 54
composite factor = 23 × 7 = 56
composite factor = 32 × 7 = 63
composite factor = 2 × 3 × 11 = 66
composite factor = 23 × 32 = 72
composite factor = 7 × 11 = 77
composite factor = 34 = 81
composite factor = 22 × 3 × 7 = 84
composite factor = 23 × 11 = 88
composite factor = 2 × 72 = 98
composite factor = 32 × 11 = 99
composite factor = 22 × 33 = 108
composite factor = 2 × 32 × 7 = 126
composite factor = 22 × 3 × 11 = 132
composite factor = 3 × 72 = 147
composite factor = 2 × 7 × 11 = 154
composite factor = 2 × 34 = 162
composite factor = 23 × 3 × 7 = 168
composite factor = 33 × 7 = 189
composite factor = 22 × 72 = 196
composite factor = 2 × 32 × 11 = 198
composite factor = 23 × 33 = 216
composite factor = 3 × 7 × 11 = 231
composite factor = 22 × 32 × 7 = 252
composite factor = 23 × 3 × 11 = 264
composite factor = 2 × 3 × 72 = 294
composite factor = 33 × 11 = 297
composite factor = 22 × 7 × 11 = 308
composite factor = 22 × 34 = 324
composite factor = 2 × 33 × 7 = 378
composite factor = 23 × 72 = 392
composite factor = 22 × 32 × 11 = 396
composite factor = 32 × 72 = 441
composite factor = 2 × 3 × 7 × 11 = 462
composite factor = 23 × 32 × 7 = 504
composite factor = 72 × 11 = 539
composite factor = 34 × 7 = 567
composite factor = 22 × 3 × 72 = 588
This list continues below...

... This list continues from above
composite factor = 2 × 33 × 11 = 594
composite factor = 23 × 7 × 11 = 616
composite factor = 23 × 34 = 648
composite factor = 32 × 7 × 11 = 693
composite factor = 22 × 33 × 7 = 756
composite factor = 23 × 32 × 11 = 792
composite factor = 2 × 32 × 72 = 882
composite factor = 34 × 11 = 891
composite factor = 22 × 3 × 7 × 11 = 924
composite factor = 2 × 72 × 11 = 1,078
composite factor = 2 × 34 × 7 = 1,134
composite factor = 23 × 3 × 72 = 1,176
composite factor = 22 × 33 × 11 = 1,188
composite factor = 33 × 72 = 1,323
composite factor = 2 × 32 × 7 × 11 = 1,386
composite factor = 23 × 33 × 7 = 1,512
composite factor = 3 × 72 × 11 = 1,617
composite factor = 22 × 32 × 72 = 1,764
composite factor = 2 × 34 × 11 = 1,782
composite factor = 23 × 3 × 7 × 11 = 1,848
composite factor = 33 × 7 × 11 = 2,079
composite factor = 22 × 72 × 11 = 2,156
composite factor = 22 × 34 × 7 = 2,268
composite factor = 23 × 33 × 11 = 2,376
composite factor = 2 × 33 × 72 = 2,646
composite factor = 22 × 32 × 7 × 11 = 2,772
composite factor = 2 × 3 × 72 × 11 = 3,234
composite factor = 23 × 32 × 72 = 3,528
composite factor = 22 × 34 × 11 = 3,564
composite factor = 34 × 72 = 3,969
composite factor = 2 × 33 × 7 × 11 = 4,158
composite factor = 23 × 72 × 11 = 4,312
composite factor = 23 × 34 × 7 = 4,536
composite factor = 32 × 72 × 11 = 4,851
composite factor = 22 × 33 × 72 = 5,292
composite factor = 23 × 32 × 7 × 11 = 5,544
composite factor = 34 × 7 × 11 = 6,237
composite factor = 22 × 3 × 72 × 11 = 6,468
composite factor = 23 × 34 × 11 = 7,128
composite factor = 2 × 34 × 72 = 7,938
composite factor = 22 × 33 × 7 × 11 = 8,316
composite factor = 2 × 32 × 72 × 11 = 9,702
composite factor = 23 × 33 × 72 = 10,584
composite factor = 2 × 34 × 7 × 11 = 12,474
composite factor = 23 × 3 × 72 × 11 = 12,936
composite factor = 33 × 72 × 11 = 14,553
composite factor = 22 × 34 × 72 = 15,876
composite factor = 23 × 33 × 7 × 11 = 16,632
composite factor = 22 × 32 × 72 × 11 = 19,404
composite factor = 22 × 34 × 7 × 11 = 24,948
composite factor = 2 × 33 × 72 × 11 = 29,106
composite factor = 23 × 34 × 72 = 31,752
composite factor = 23 × 32 × 72 × 11 = 38,808
composite factor = 34 × 72 × 11 = 43,659
composite factor = 23 × 34 × 7 × 11 = 49,896
composite factor = 22 × 33 × 72 × 11 = 58,212
composite factor = 2 × 34 × 72 × 11 = 87,318
composite factor = 23 × 33 × 72 × 11 = 116,424
composite factor = 22 × 34 × 72 × 11 = 174,636
composite factor = 23 × 34 × 72 × 11 = 349,272
120 factors (divisors)

What times what is 349,272?
What number multiplied by what number equals 349,272?

All the combinations of any two natural numbers whose product equals 349,272.

1 × 349,272 = 349,272
2 × 174,636 = 349,272
3 × 116,424 = 349,272
4 × 87,318 = 349,272
6 × 58,212 = 349,272
7 × 49,896 = 349,272
8 × 43,659 = 349,272
9 × 38,808 = 349,272
11 × 31,752 = 349,272
12 × 29,106 = 349,272
14 × 24,948 = 349,272
18 × 19,404 = 349,272
21 × 16,632 = 349,272
22 × 15,876 = 349,272
24 × 14,553 = 349,272
27 × 12,936 = 349,272
28 × 12,474 = 349,272
33 × 10,584 = 349,272
36 × 9,702 = 349,272
42 × 8,316 = 349,272
44 × 7,938 = 349,272
49 × 7,128 = 349,272
54 × 6,468 = 349,272
56 × 6,237 = 349,272
63 × 5,544 = 349,272
66 × 5,292 = 349,272
72 × 4,851 = 349,272
77 × 4,536 = 349,272
81 × 4,312 = 349,272
84 × 4,158 = 349,272
88 × 3,969 = 349,272
98 × 3,564 = 349,272
99 × 3,528 = 349,272
108 × 3,234 = 349,272
126 × 2,772 = 349,272
132 × 2,646 = 349,272
147 × 2,376 = 349,272
154 × 2,268 = 349,272
162 × 2,156 = 349,272
168 × 2,079 = 349,272
189 × 1,848 = 349,272
196 × 1,782 = 349,272
198 × 1,764 = 349,272
216 × 1,617 = 349,272
231 × 1,512 = 349,272
252 × 1,386 = 349,272
264 × 1,323 = 349,272
294 × 1,188 = 349,272
297 × 1,176 = 349,272
308 × 1,134 = 349,272
324 × 1,078 = 349,272
378 × 924 = 349,272
392 × 891 = 349,272
396 × 882 = 349,272
441 × 792 = 349,272
462 × 756 = 349,272
504 × 693 = 349,272
539 × 648 = 349,272
567 × 616 = 349,272
588 × 594 = 349,272
60 unique multiplications

The final answer:
(scroll down)


349,272 has 120 factors (divisors):
1; 2; 3; 4; 6; 7; 8; 9; 11; 12; 14; 18; 21; 22; 24; 27; 28; 33; 36; 42; 44; 49; 54; 56; 63; 66; 72; 77; 81; 84; 88; 98; 99; 108; 126; 132; 147; 154; 162; 168; 189; 196; 198; 216; 231; 252; 264; 294; 297; 308; 324; 378; 392; 396; 441; 462; 504; 539; 567; 588; 594; 616; 648; 693; 756; 792; 882; 891; 924; 1,078; 1,134; 1,176; 1,188; 1,323; 1,386; 1,512; 1,617; 1,764; 1,782; 1,848; 2,079; 2,156; 2,268; 2,376; 2,646; 2,772; 3,234; 3,528; 3,564; 3,969; 4,158; 4,312; 4,536; 4,851; 5,292; 5,544; 6,237; 6,468; 7,128; 7,938; 8,316; 9,702; 10,584; 12,474; 12,936; 14,553; 15,876; 16,632; 19,404; 24,948; 29,106; 31,752; 38,808; 43,659; 49,896; 58,212; 87,318; 116,424; 174,636 and 349,272
out of which 4 prime factors: 2; 3; 7 and 11.
Numbers other than 1 that are not prime factors are composite factors (divisors).
349,272 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.

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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".