What is the Greatest Common Factor of 48096 and 48114?

Greatest common factor (GCF) of 48096 and 48114 is 18.

GCF(48096,48114) = 18

We will now calculate the prime factors of 48096 and 48114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48096 and 48114.

How to find the GCF of 48096 and 48114?

We will first find the prime factorization of 48096 and 48114. After we will calculate the factors of 48096 and 48114 and find the biggest common factor number .

Step-1: Prime Factorization of 48096

Prime factors of 48096 are 2, 3, 167. Prime factorization of 48096 in exponential form is:

48096 = 2⁵ × 3² × 167¹

Step-2: Prime Factorization of 48114

Prime factors of 48114 are 2, 3, 11. Prime factorization of 48114 in exponential form is:

48114 = 2¹ × 3⁷ × 11¹

Step-3: Factors of 48096

List of positive integer factors of 48096 that divides 48096 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 167, 288, 334, 501, 668, 1002, 1336, 1503, 2004, 2672, 3006, 4008, 5344, 6012, 8016, 12024, 16032, 24048

Step-4: Factors of 48114

List of positive integer factors of 48114 that divides 48096 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 27, 33, 54, 66, 81, 99, 162, 198, 243, 297, 486, 594, 729, 891, 1458, 1782, 2187, 2673, 4374, 5346, 8019, 16038, 24057

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48096 and 48114. The biggest common factor number is the GCF number.
So the greatest common factor 48096 and 48114 is 18.

Also check out the Least Common Multiple of 48096 and 48114