What is the Greatest Common Factor of 45 and 165?

Greatest common factor (GCF) of 45 and 165 is 15.

GCF(45,165) = 15

We will now calculate the prime factors of 45 and 165, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45 and 165.

How to find the GCF of 45 and 165?

We will first find the prime factorization of 45 and 165. After we will calculate the factors of 45 and 165 and find the biggest common factor number .

Step-1: Prime Factorization of 45

Prime factors of 45 are 3, 5. Prime factorization of 45 in exponential form is:

45 = 3² × 5¹

Step-2: Prime Factorization of 165

Prime factors of 165 are 3, 5, 11. Prime factorization of 165 in exponential form is:

165 = 3¹ × 5¹ × 11¹

Step-3: Factors of 45

List of positive integer factors of 45 that divides 45 without a remainder.

1, 3, 5, 9, 15

Step-4: Factors of 165

List of positive integer factors of 165 that divides 45 without a remainder.

1, 3, 5, 11, 15, 33, 55

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45 and 165. The biggest common factor number is the GCF number.
So the greatest common factor 45 and 165 is 15.

Also check out the Least Common Multiple of 45 and 165