Calculate the greatest (highest) common factor (divisor).
Follow the two steps below.
1. Carry out the prime factorization of the two numbers:
The prime factorization of a number: finding the prime numbers that multiply together to make that number.
21,392 = 24 × 7 × 191
21,392 is not a prime number but a composite one.
39,728 = 24 × 13 × 191
39,728 is not a prime number but a composite one.
* Prime number: a natural number that is divisible only by 1 and itself. A prime number has exactly two factors: 1 and itself.
* Composite number: a natural number that has at least one other factor than 1 and itself.
2. Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd:
Multiply all the common prime factors, taken by their smallest exponents (the smallest powers).
gcf, hcf, gcd (21,392; 39,728) = 24 × 191 = 3,056
How to count the number of factors of a number?
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 = (4 + 1) × (1 + 1) = 5 × 2 = 10
But to actually calculate the factors, see below...
3. Multiply the prime factors of the 'gcf':
Multiply the prime factors involved in the prime factorization of the GCF in all their unique combinations, that give different results.
Also consider the exponents of the prime factors (example: 32 = 3 × 3 = 9).
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
2
2 =
4
2
3 =
8
2
4 =
16
This list continues below...