What is the Greatest Common Factor of 36138 and 36144?

Greatest common factor (GCF) of 36138 and 36144 is 6.

GCF(36138,36144) = 6

We will now calculate the prime factors of 36138 and 36144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36138 and 36144.

How to find the GCF of 36138 and 36144?

We will first find the prime factorization of 36138 and 36144. After we will calculate the factors of 36138 and 36144 and find the biggest common factor number .

Step-1: Prime Factorization of 36138

Prime factors of 36138 are 2, 3, 19, 317. Prime factorization of 36138 in exponential form is:

36138 = 2¹ × 3¹ × 19¹ × 317¹

Step-2: Prime Factorization of 36144

Prime factors of 36144 are 2, 3, 251. Prime factorization of 36144 in exponential form is:

36144 = 2⁴ × 3² × 251¹

Step-3: Factors of 36138

List of positive integer factors of 36138 that divides 36138 without a remainder.

1, 2, 3, 6, 19, 38, 57, 114, 317, 634, 951, 1902, 6023, 12046, 18069

Step-4: Factors of 36144

List of positive integer factors of 36144 that divides 36138 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 251, 502, 753, 1004, 1506, 2008, 2259, 3012, 4016, 4518, 6024, 9036, 12048, 18072

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36138 and 36144. The biggest common factor number is the GCF number.
So the greatest common factor 36138 and 36144 is 6.

Also check out the Least Common Multiple of 36138 and 36144