What is the Greatest Common Factor of 175 and 189?

Greatest common factor (GCF) of 175 and 189 is 7.

GCF(175,189) = 7

We will now calculate the prime factors of 175 and 189, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 175 and 189.

How to find the GCF of 175 and 189?

We will first find the prime factorization of 175 and 189. After we will calculate the factors of 175 and 189 and find the biggest common factor number .

Step-1: Prime Factorization of 175

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

175 = 5² × 7¹

Step-2: Prime Factorization of 189

Prime factors of 189 are 3, 7. Prime factorization of 189 in exponential form is:

189 = 3³ × 7¹

Step-3: Factors of 175

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

1, 5, 7, 25, 35

Step-4: Factors of 189

List of positive integer factors of 189 that divides 175 without a remainder.

1, 3, 7, 9, 21, 27, 63

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 175 and 189. The biggest common factor number is the GCF number.
So the greatest common factor 175 and 189 is 7.

Also check out the Least Common Multiple of 175 and 189