What is the Greatest Common Factor of 42120 and 42140?

Greatest common factor (GCF) of 42120 and 42140 is 20.

GCF(42120,42140) = 20

We will now calculate the prime factors of 42120 and 42140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42120 and 42140.

How to find the GCF of 42120 and 42140?

We will first find the prime factorization of 42120 and 42140. After we will calculate the factors of 42120 and 42140 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 42140

Prime factors of 42140 are 2, 5, 7, 43. Prime factorization of 42140 in exponential form is:

42140 = 2² × 5¹ × 7² × 43¹

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 42140

List of positive integer factors of 42140 that divides 42120 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 43, 49, 70, 86, 98, 140, 172, 196, 215, 245, 301, 430, 490, 602, 860, 980, 1204, 1505, 2107, 3010, 4214, 6020, 8428, 10535, 21070

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42120 and 42140. The biggest common factor number is the GCF number.
So the greatest common factor 42120 and 42140 is 20.

Also check out the Least Common Multiple of 42120 and 42140