What is the Greatest Common Factor of 38160 and 38172?

Greatest common factor (GCF) of 38160 and 38172 is 12.

GCF(38160,38172) = 12

We will now calculate the prime factors of 38160 and 38172, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38160 and 38172.

How to find the GCF of 38160 and 38172?

We will first find the prime factorization of 38160 and 38172. After we will calculate the factors of 38160 and 38172 and find the biggest common factor number .

Step-1: Prime Factorization of 38160

Prime factors of 38160 are 2, 3, 5, 53. Prime factorization of 38160 in exponential form is:

38160 = 2⁴ × 3² × 5¹ × 53¹

Step-2: Prime Factorization of 38172

Prime factors of 38172 are 2, 3, 3181. Prime factorization of 38172 in exponential form is:

38172 = 2² × 3¹ × 3181¹

Step-3: Factors of 38160

List of positive integer factors of 38160 that divides 38160 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 53, 60, 72, 80, 90, 106, 120, 144, 159, 180, 212, 240, 265, 318, 360, 424, 477, 530, 636, 720, 795, 848, 954, 1060, 1272, 1590, 1908, 2120, 2385, 2544, 3180, 3816, 4240, 4770, 6360, 7632, 9540, 12720, 19080

Step-4: Factors of 38172

List of positive integer factors of 38172 that divides 38160 without a remainder.

1, 2, 3, 4, 6, 12, 3181, 6362, 9543, 12724, 19086

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38160 and 38172. The biggest common factor number is the GCF number.
So the greatest common factor 38160 and 38172 is 12.

Also check out the Least Common Multiple of 38160 and 38172