What is the GCF of 75 and 90?
Greatest Common Factor is the biggest number, that is a factor of the given numbers.
The GCF (greatest common factor) is the same as: HCF (Highest Common Factor), GCD (Greatest Common Divisor), HCD (Highest Common Divisor), GCM (Greatest Common Measure), HCM (Highest Common Measure)
Answer: GCF of 75 and 90 is 15
Two methods to find the GCF of 75 and 90 are explained below.
Methods to find GCF of 75 and 90
- Prime Factorization
- Long Division
Method 1: GCF of 75 and 90 by Prime Factorization
GCF is the product of the factors that are common to each of the given numbers.
Prime factorization of 75 is 3 × 5 × 5
Prime factorization of 90 is 2 × 3 × 3 × 5
The occurrences of common prime factors of 75 and 90 are 3 and 5
Hence GCF(75, 90) is 3 × 5 = 15
Method 2: GCF of 75 and 90 by Long Division
- Step 1: Divide the larger number by the smaller
- Step 2: Divide the dividend by the remainder obtained in step 1 and repeat this step until we get the remainder as 0
- Step 3: The last dividend is the GCF of the two numbers
We take the larger value 90 as dividend and smaller value 75 as divisor
We will get the GCF same for the given numbers by using different methods.