What is the Greatest Common Factor of 72114 and 72120?

Greatest common factor (GCF) of 72114 and 72120 is 6.

GCF(72114,72120) = 6

We will now calculate the prime factors of 72114 and 72120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72114 and 72120.

How to find the GCF of 72114 and 72120?

We will first find the prime factorization of 72114 and 72120. After we will calculate the factors of 72114 and 72120 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 72120

Prime factors of 72120 are 2, 3, 5, 601. Prime factorization of 72120 in exponential form is:

72120 = 2³ × 3¹ × 5¹ × 601¹

Step-3: Factors of 72114

List of positive integer factors of 72114 that divides 72114 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

Step-4: Factors of 72120

List of positive integer factors of 72120 that divides 72114 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 601, 1202, 1803, 2404, 3005, 3606, 4808, 6010, 7212, 9015, 12020, 14424, 18030, 24040, 36060

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72114 and 72120. The biggest common factor number is the GCF number.
So the greatest common factor 72114 and 72120 is 6.

Also check out the Least Common Multiple of 72114 and 72120