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.
52,501,372 = 22 × 7 × 11 × 17 × 37 × 271
52,501,372 is not a prime number but a composite one.
97,502,548 = 22 × 11 × 13 × 17 × 37 × 271
97,502,548 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 (52,501,372; 97,502,548) = 22 × 11 × 17 × 37 × 271 = 7,500,196
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 = (2 + 1) × (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 × 2 × 2 = 48
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
prime factor =
11
prime factor =
17
2 × 11 =
22
2 × 17 =
34
prime factor =
37
2
2 × 11 =
44
2
2 × 17 =
68
2 × 37 =
74
2
2 × 37 =
148
11 × 17 =
187
prime factor =
271
2 × 11 × 17 =
374
11 × 37 =
407
2 × 271 =
542
17 × 37 =
629
2
2 × 11 × 17 =
748
2 × 11 × 37 =
814
2
2 × 271 =
1,084
2 × 17 × 37 =
1,258
2
2 × 11 × 37 =
1,628
2
2 × 17 × 37 =
2,516
This list continues below...