What is the Greatest Common Factor of 54144 and 54164?

Greatest common factor (GCF) of 54144 and 54164 is 4.

GCF(54144,54164) = 4

We will now calculate the prime factors of 54144 and 54164, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54144 and 54164.

How to find the GCF of 54144 and 54164?

We will first find the prime factorization of 54144 and 54164. After we will calculate the factors of 54144 and 54164 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 54164

Prime factors of 54164 are 2, 11, 1231. Prime factorization of 54164 in exponential form is:

54164 = 2² × 11¹ × 1231¹

Step-3: Factors of 54144

List of positive integer factors of 54144 that divides 54144 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

Step-4: Factors of 54164

List of positive integer factors of 54164 that divides 54144 without a remainder.

1, 2, 4, 11, 22, 44, 1231, 2462, 4924, 13541, 27082

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54144 and 54164. The biggest common factor number is the GCF number.
So the greatest common factor 54144 and 54164 is 4.

Also check out the Least Common Multiple of 54144 and 54164