What is the Greatest Common Factor of 135 and 144?

Greatest common factor (GCF) of 135 and 144 is 9.

GCF(135,144) = 9

We will now calculate the prime factors of 135 and 144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 135 and 144.

How to find the GCF of 135 and 144?

We will first find the prime factorization of 135 and 144. After we will calculate the factors of 135 and 144 and find the biggest common factor number .

Step-1: Prime Factorization of 135

Prime factors of 135 are 3, 5. Prime factorization of 135 in exponential form is:

135 = 3³ × 5¹

Step-2: Prime Factorization of 144

Prime factors of 144 are 2, 3. Prime factorization of 144 in exponential form is:

144 = 2⁴ × 3²

Step-3: Factors of 135

List of positive integer factors of 135 that divides 135 without a remainder.

1, 3, 5, 9, 15, 27, 45

Step-4: Factors of 144

List of positive integer factors of 144 that divides 135 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 135 and 144. The biggest common factor number is the GCF number.
So the greatest common factor 135 and 144 is 9.

Also check out the Least Common Multiple of 135 and 144