What is the Greatest Common Factor of 54132 and 54144?

Greatest common factor (GCF) of 54132 and 54144 is 12.

GCF(54132,54144) = 12

We will now calculate the prime factors of 54132 and 54144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54132 and 54144.

How to find the GCF of 54132 and 54144?

We will first find the prime factorization of 54132 and 54144. After we will calculate the factors of 54132 and 54144 and find the biggest common factor number .

Step-1: Prime Factorization of 54132

Prime factors of 54132 are 2, 3, 13, 347. Prime factorization of 54132 in exponential form is:

54132 = 2² × 3¹ × 13¹ × 347¹

Step-2: Prime Factorization of 54144

Prime factors of 54144 are 2, 3, 47. Prime factorization of 54144 in exponential form is:

54144 = 2⁷ × 3² × 47¹

Step-3: Factors of 54132

List of positive integer factors of 54132 that divides 54132 without a remainder.

1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156, 347, 694, 1041, 1388, 2082, 4164, 4511, 9022, 13533, 18044, 27066

Step-4: Factors of 54144

List of positive integer factors of 54144 that divides 54132 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 47, 48, 64, 72, 94, 96, 128, 141, 144, 188, 192, 282, 288, 376, 384, 423, 564, 576, 752, 846, 1128, 1152, 1504, 1692, 2256, 3008, 3384, 4512, 6016, 6768, 9024, 13536, 18048, 27072

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54132 and 54144. The biggest common factor number is the GCF number.
So the greatest common factor 54132 and 54144 is 12.

Also check out the Least Common Multiple of 54132 and 54144