What is the Greatest Common Factor of 42120 and 42135?

Greatest common factor (GCF) of 42120 and 42135 is 15.

GCF(42120,42135) = 15

We will now calculate the prime factors of 42120 and 42135, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42120 and 42135.

How to find the GCF of 42120 and 42135?

We will first find the prime factorization of 42120 and 42135. After we will calculate the factors of 42120 and 42135 and find the biggest common factor number .

Step-1: Prime Factorization of 42120

Prime factors of 42120 are 2, 3, 5, 13. Prime factorization of 42120 in exponential form is:

42120 = 2³ × 3⁴ × 5¹ × 13¹

Step-2: Prime Factorization of 42135

Prime factors of 42135 are 3, 5, 53. Prime factorization of 42135 in exponential form is:

42135 = 3¹ × 5¹ × 53²

Step-3: Factors of 42120

List of positive integer factors of 42120 that divides 42120 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 18, 20, 24, 26, 27, 30, 36, 39, 40, 45, 52, 54, 60, 65, 72, 78, 81, 90, 104, 108, 117, 120, 130, 135, 156, 162, 180, 195, 216, 234, 260, 270, 312, 324, 351, 360, 390, 405, 468, 520, 540, 585, 648, 702, 780, 810, 936, 1053, 1080, 1170, 1404, 1560, 1620, 1755, 2106, 2340, 2808, 3240, 3510, 4212, 4680, 5265, 7020, 8424, 10530, 14040, 21060

Step-4: Factors of 42135

List of positive integer factors of 42135 that divides 42120 without a remainder.

1, 3, 5, 15, 53, 159, 265, 795, 2809, 8427, 14045

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42120 and 42135. The biggest common factor number is the GCF number.
So the greatest common factor 42120 and 42135 is 15.

Also check out the Least Common Multiple of 42120 and 42135