What is the Greatest Common Factor of 144 and 300?

Greatest common factor (GCF) of 144 and 300 is 12.

GCF(144,300) = 12

We will now calculate the prime factors of 144 and 300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 144 and 300.

How to find the GCF of 144 and 300?

We will first find the prime factorization of 144 and 300. After we will calculate the factors of 144 and 300 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 300

Prime factors of 300 are 2, 3, 5. Prime factorization of 300 in exponential form is:

300 = 2² × 3¹ × 5²

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 300

List of positive integer factors of 300 that divides 144 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 144 and 300. The biggest common factor number is the GCF number.
So the greatest common factor 144 and 300 is 12.

Also check out the Least Common Multiple of 144 and 300