What is the Greatest Common Factor of 177 and 192?

Greatest common factor (GCF) of 177 and 192 is 3.

GCF(177,192) = 3

We will now calculate the prime factors of 177 and 192, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 177 and 192.

How to find the GCF of 177 and 192?

We will first find the prime factorization of 177 and 192. After we will calculate the factors of 177 and 192 and find the biggest common factor number .

Step-1: Prime Factorization of 177

Prime factors of 177 are 3, 59. Prime factorization of 177 in exponential form is:

177 = 3¹ × 59¹

Step-2: Prime Factorization of 192

Prime factors of 192 are 2, 3. Prime factorization of 192 in exponential form is:

192 = 2⁶ × 3¹

Step-3: Factors of 177

List of positive integer factors of 177 that divides 177 without a remainder.

1, 3, 59

Step-4: Factors of 192

List of positive integer factors of 192 that divides 177 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 177 and 192. The biggest common factor number is the GCF number.
So the greatest common factor 177 and 192 is 3.

Also check out the Least Common Multiple of 177 and 192