What is the Greatest Common Factor of 192 and 200?

Greatest common factor (GCF) of 192 and 200 is 8.

GCF(192,200) = 8

We will now calculate the prime factors of 192 and 200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 192 and 200.

How to find the GCF of 192 and 200?

We will first find the prime factorization of 192 and 200. After we will calculate the factors of 192 and 200 and find the biggest common factor number .

Step-1: Prime Factorization of 192

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

192 = 2⁶ × 3¹

Step-2: Prime Factorization of 200

Prime factors of 200 are 2, 5. Prime factorization of 200 in exponential form is:

200 = 2³ × 5²

Step-3: Factors of 192

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

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

Step-4: Factors of 200

List of positive integer factors of 200 that divides 192 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 192 and 200. The biggest common factor number is the GCF number.
So the greatest common factor 192 and 200 is 8.

Also check out the Least Common Multiple of 192 and 200