Calculate GCF (4; 60,320), the Greatest (Highest) Common Factor (Divisor), (HCF, GCD), of the Numbers. Online Calculator
Calculate the greatest common factor, GCF (4; 60,320), using their prime factorizations, numbers' divisibility or the Euclidean algorithm
Method 1. The divisibility of numbers:
Divide the larger number by the smaller one.
Note that when the numbers are divided, the remainder is zero:
60,320 ÷ 4 = 15,080 + 0
⇒ 60,320 = 4 × 15,080
So, 60,320 is divisible by 4.
And 4 is a factor (divisor) of 60,320.
Also, the greatest factor (divisor) of 4 is the number itself, 4.
The greatest (highest) common factor (divisor),
gcf, hcf, gcd (4; 60,320) = 4 = 22
60,320 is divisible by 4
Scroll down for the 2nd method...
Method 2. The prime factorization:
The prime factorization of a number: finding the prime numbers that multiply together to make that number.
4 = 22
4 is not a prime number but a composite one.
60,320 = 25 × 5 × 13 × 29
60,320 is not a prime number but a composite one.
* Prime number: a natural number that is only divisible 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.
Calculate the greatest (highest) common factor (divisor):
Multiply all the common prime factors, taken by their smallest exponents (the smallest powers).
The greatest (highest) common factor (divisor),
gcf, hcf, gcd (4; 60,320) = 22 = 4
60,320 contains all the prime factors of the number 4
60,320 is divisible by 4.
Why do we need to calculate the greatest common factor?
Once you've calculated the greatest common factor of the numerator and the denominator of a fraction, it becomes much easier to fully reduce (simplify) the fraction to the lowest terms (the smallest possible numerator and denominator).
Other similar operations with the greatest (highest) common factor (divisor):