What is the Greatest Common Factor of 172 and 176?

Greatest common factor (GCF) of 172 and 176 is 4.

GCF(172,176) = 4

We will now calculate the prime factors of 172 and 176, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 172 and 176.

How to find the GCF of 172 and 176?

We will first find the prime factorization of 172 and 176. After we will calculate the factors of 172 and 176 and find the biggest common factor number .

Step-1: Prime Factorization of 172

Prime factors of 172 are 2, 43. Prime factorization of 172 in exponential form is:

172 = 2² × 43¹

Step-2: Prime Factorization of 176

Prime factors of 176 are 2, 11. Prime factorization of 176 in exponential form is:

176 = 2⁴ × 11¹

Step-3: Factors of 172

List of positive integer factors of 172 that divides 172 without a remainder.

1, 2, 4, 43, 86

Step-4: Factors of 176

List of positive integer factors of 176 that divides 172 without a remainder.

1, 2, 4, 8, 11, 16, 22, 44, 88

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 172 and 176. The biggest common factor number is the GCF number.
So the greatest common factor 172 and 176 is 4.

Also check out the Least Common Multiple of 172 and 176