What is the Greatest Common Factor of 72108 and 72114?

Greatest common factor (GCF) of 72108 and 72114 is 6.

GCF(72108,72114) = 6

We will now calculate the prime factors of 72108 and 72114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72108 and 72114.

How to find the GCF of 72108 and 72114?

We will first find the prime factorization of 72108 and 72114. After we will calculate the factors of 72108 and 72114 and find the biggest common factor number .

Step-1: Prime Factorization of 72108

Prime factors of 72108 are 2, 3, 2003. Prime factorization of 72108 in exponential form is:

72108 = 2² × 3² × 2003¹

Step-2: Prime Factorization of 72114

Prime factors of 72114 are 2, 3, 7, 17, 101. Prime factorization of 72114 in exponential form is:

72114 = 2¹ × 3¹ × 7¹ × 17¹ × 101¹

Step-3: Factors of 72108

List of positive integer factors of 72108 that divides 72108 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 2003, 4006, 6009, 8012, 12018, 18027, 24036, 36054

Step-4: Factors of 72114

List of positive integer factors of 72114 that divides 72108 without a remainder.

1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 101, 102, 119, 202, 238, 303, 357, 606, 707, 714, 1414, 1717, 2121, 3434, 4242, 5151, 10302, 12019, 24038, 36057

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72108 and 72114. The biggest common factor number is the GCF number.
So the greatest common factor 72108 and 72114 is 6.

Also check out the Least Common Multiple of 72108 and 72114