What is the Greatest Common Factor of 168 and 175?

Greatest common factor (GCF) of 168 and 175 is 7.

GCF(168,175) = 7

We will now calculate the prime factors of 168 and 175, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 168 and 175.

How to find the GCF of 168 and 175?

We will first find the prime factorization of 168 and 175. After we will calculate the factors of 168 and 175 and find the biggest common factor number .

Step-1: Prime Factorization of 168

Prime factors of 168 are 2, 3, 7. Prime factorization of 168 in exponential form is:

168 = 2³ × 3¹ × 7¹

Step-2: Prime Factorization of 175

Prime factors of 175 are 5, 7. Prime factorization of 175 in exponential form is:

175 = 5² × 7¹

Step-3: Factors of 168

List of positive integer factors of 168 that divides 168 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84

Step-4: Factors of 175

List of positive integer factors of 175 that divides 168 without a remainder.

1, 5, 7, 25, 35

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 168 and 175. The biggest common factor number is the GCF number.
So the greatest common factor 168 and 175 is 7.

Also check out the Least Common Multiple of 168 and 175