What is the Greatest Common Factor of 208 and 225?

Greatest common factor (GCF) of 208 and 225 is 1.

GCF(208,225) = 1

We will now calculate the prime factors of 208 and 225, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 208 and 225.

How to find the GCF of 208 and 225?

We will first find the prime factorization of 208 and 225. After we will calculate the factors of 208 and 225 and find the biggest common factor number .

Step-1: Prime Factorization of 208

Prime factors of 208 are 2, 13. Prime factorization of 208 in exponential form is:

208 = 2⁴ × 13¹

Step-2: Prime Factorization of 225

Prime factors of 225 are 3, 5. Prime factorization of 225 in exponential form is:

225 = 3² × 5²

Step-3: Factors of 208

List of positive integer factors of 208 that divides 208 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 104

Step-4: Factors of 225

List of positive integer factors of 225 that divides 208 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 208 and 225. The biggest common factor number is the GCF number.
So the greatest common factor 208 and 225 is 1.

Also check out the Least Common Multiple of 208 and 225