What is the Greatest Common Factor of 175 and 195?

Greatest common factor (GCF) of 175 and 195 is 5.

GCF(175,195) = 5

We will now calculate the prime factors of 175 and 195, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 175 and 195.

How to find the GCF of 175 and 195?

We will first find the prime factorization of 175 and 195. After we will calculate the factors of 175 and 195 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 195

Prime factors of 195 are 3, 5, 13. Prime factorization of 195 in exponential form is:

195 = 3¹ × 5¹ × 13¹

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 195

List of positive integer factors of 195 that divides 175 without a remainder.

1, 3, 5, 13, 15, 39, 65

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 175 and 195. The biggest common factor number is the GCF number.
So the greatest common factor 175 and 195 is 5.

Also check out the Least Common Multiple of 175 and 195