What is the Greatest Common Factor of 36126 and 36144?

Greatest common factor (GCF) of 36126 and 36144 is 18.

GCF(36126,36144) = 18

We will now calculate the prime factors of 36126 and 36144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36126 and 36144.

How to find the GCF of 36126 and 36144?

We will first find the prime factorization of 36126 and 36144. After we will calculate the factors of 36126 and 36144 and find the biggest common factor number .

Step-1: Prime Factorization of 36126

Prime factors of 36126 are 2, 3, 223. Prime factorization of 36126 in exponential form is:

36126 = 2¹ × 3⁴ × 223¹

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 36126

List of positive integer factors of 36126 that divides 36126 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 223, 446, 669, 1338, 2007, 4014, 6021, 12042, 18063

Step-4: Factors of 36144

List of positive integer factors of 36144 that divides 36126 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 36126 and 36144. The biggest common factor number is the GCF number.
So the greatest common factor 36126 and 36144 is 18.

Also check out the Least Common Multiple of 36126 and 36144