The common factors (divisors) of the numbers 683,356,492 and 1,000,000,000,000?
The common factors of the numbers 683,356,492 and 1,000,000,000,000 are all the factors of their 'greatest common factor', gcf
Calculate the greatest (highest) common factor (divisor).
Follow the two steps below.
1. Perform the prime factorization of the two numbers:
The prime factorization of a number: finding the prime numbers that multiply together to make that number.
683,356,492 = 22 × 7 × 13 × 1,877,353
683,356,492 is not a prime number but a composite one.
1,000,000,000,000 = 212 × 512
1,000,000,000,000 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 (683,356,492; 1,000,000,000,000) = 22 = 4
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) = 3 = 3
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