Calculate GCF (85; 17), the Greatest (Highest) Common Factor (Divisor), (HCF, GCD), of the Numbers. Online Calculator
Calculate the greatest common factor, GCF (85; 17), 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:
85 ÷ 17 = 5 + 0
⇒ 85 = 17 × 5
So, 85 is divisible by 17.
And 17 is a factor (divisor) of 85.
Also, the greatest factor (divisor) of 17 is the number itself, 17.
The greatest (highest) common factor (divisor),
gcf, hcf, gcd (85; 17) = 17
85 is divisible by 17
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.
85 = 5 × 17
85 is not a prime number but a composite one.
17 is a prime number and cannot be broken down into other prime factors.
* 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 (85; 17) = 17
85 contains all the prime factors of the number 17
85 is divisible by 17.
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):