What is the Greatest Common Factor of 144 and 152?

Greatest common factor (GCF) of 144 and 152 is 8.

GCF(144,152) = 8

We will now calculate the prime factors of 144 and 152, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 144 and 152.

How to find the GCF of 144 and 152?

We will first find the prime factorization of 144 and 152. After we will calculate the factors of 144 and 152 and find the biggest common factor number .

Step-1: Prime Factorization of 144

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

144 = 2⁴ × 3²

Step-2: Prime Factorization of 152

Prime factors of 152 are 2, 19. Prime factorization of 152 in exponential form is:

152 = 2³ × 19¹

Step-3: Factors of 144

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

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

Step-4: Factors of 152

List of positive integer factors of 152 that divides 144 without a remainder.

1, 2, 4, 8, 19, 38, 76

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 144 and 152. The biggest common factor number is the GCF number.
So the greatest common factor 144 and 152 is 8.

Also check out the Least Common Multiple of 144 and 152