12,480: Calculate all the factors (divisors) of the number (proper, improper and the prime factors)

The factors (divisors) of the number 12,480

12,480 is a composite number and can be prime factorized. So what are all the factors (divisors) of the number 12,480?

A factor (a divisor) of the number 12,480 is a natural number B which when multiplied by another natural number C equals the given number 12,480:
12,480 = B × C. Example: 60 = 2 × 30.

Both B and C are factors of 12,480.


To find all the factors (divisors) of the number 12,480:

1) Break down the number into its prime factors (build the number's prime factorization, decompose it into prime factors, write it as a product of prime numbers).

2) Then multiply these prime factors in all their unique combinations, that yield different results.



1) The prime factorization:

The prime factorization of the number 12,480 (the decomposition of the number into prime factors, breaking the number down into prime numbers) = dividing the number 12,480 into smaller, prime numbers. The number 12,480 results from the multiplication of these prime numbers.


12,480 = 26 × 3 × 5 × 13
12,480 is not a prime number but a composite one.


* The natural numbers that are divisible (that are divided evenly) only by 1 and themselves are called prime numbers. Examples: 2, 3, 5, 7, 11, 13, 17. A prime number has exactly two factors: 1 and the number itself.
* A composite number is a natural number that has at least one factor other than 1 and itself. Examples: 4, 6, 8, 9, 10, 12, 14.




2) How do I find all the factors (divisors) of the number?

Multiply the prime factors involved in the prime factorization of the number in all their unique combinations, that give different results.


12,480 = 26 × 3 × 5 × 13


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
2 × 5 = 10
22 × 3 = 12
prime factor = 13
3 × 5 = 15
24 = 16
22 × 5 = 20
23 × 3 = 24
2 × 13 = 26
2 × 3 × 5 = 30
25 = 32
3 × 13 = 39
23 × 5 = 40
24 × 3 = 48
22 × 13 = 52
22 × 3 × 5 = 60
26 = 64
5 × 13 = 65
2 × 3 × 13 = 78
24 × 5 = 80
25 × 3 = 96
23 × 13 = 104
This list continues below...

... This list continues from above
23 × 3 × 5 = 120
2 × 5 × 13 = 130
22 × 3 × 13 = 156
25 × 5 = 160
26 × 3 = 192
3 × 5 × 13 = 195
24 × 13 = 208
24 × 3 × 5 = 240
22 × 5 × 13 = 260
23 × 3 × 13 = 312
26 × 5 = 320
2 × 3 × 5 × 13 = 390
25 × 13 = 416
25 × 3 × 5 = 480
23 × 5 × 13 = 520
24 × 3 × 13 = 624
22 × 3 × 5 × 13 = 780
26 × 13 = 832
26 × 3 × 5 = 960
24 × 5 × 13 = 1,040
25 × 3 × 13 = 1,248
23 × 3 × 5 × 13 = 1,560
25 × 5 × 13 = 2,080
26 × 3 × 13 = 2,496
24 × 3 × 5 × 13 = 3,120
26 × 5 × 13 = 4,160
25 × 3 × 5 × 13 = 6,240
26 × 3 × 5 × 13 = 12,480

The final answer:
(scroll down)

12,480 has 56 factors (divisors):
1; 2; 3; 4; 5; 6; 8; 10; 12; 13; 15; 16; 20; 24; 26; 30; 32; 39; 40; 48; 52; 60; 64; 65; 78; 80; 96; 104; 120; 130; 156; 160; 192; 195; 208; 240; 260; 312; 320; 390; 416; 480; 520; 624; 780; 832; 960; 1,040; 1,248; 1,560; 2,080; 2,496; 3,120; 4,160; 6,240 and 12,480
out of which 4 prime factors: 2; 3; 5 and 13
12,480 and 1 are called by some authors improper factors (improper divisors), 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.


The latest 5 sets of calculated factors (divisors): of one number or the common factors of two numbers

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The factors (divisors) of 12,480 = ? Feb 02 01:52 UTC (GMT)
The common factors (divisors) of 5,630,684 and 0 = ? Feb 02 01:52 UTC (GMT)
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The list of all the calculated factors (divisors) of one or two numbers

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.

Factors (divisors), common factors (common divisors), the greatest common factor, GCF (also called the greatest common divisor, GCD, or the highest common factor, HCF)

Some articles on the prime numbers

What is a prime number? Definition, examples

What is a composite number? Definition, examples

The prime numbers up to 1,000

The prime numbers up to 10,000

The Sieve of Eratosthenes

The Euclidean Algorithm

Completely reduce (simplify) fractions to the lowest terms: Steps and Examples