What is the Greatest Common Factor of 42109 and 42120?

Greatest common factor (GCF) of 42109 and 42120 is 1.

GCF(42109,42120) = 1

We will now calculate the prime factors of 42109 and 42120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42109 and 42120.

How to find the GCF of 42109 and 42120?

We will first find the prime factorization of 42109 and 42120. After we will calculate the factors of 42109 and 42120 and find the biggest common factor number .

Step-1: Prime Factorization of 42109

Prime factors of 42109 are 17, 2477. Prime factorization of 42109 in exponential form is:

42109 = 17¹ × 2477¹

Step-2: 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-3: Factors of 42109

List of positive integer factors of 42109 that divides 42109 without a remainder.

1, 17, 2477

Step-4: Factors of 42120

List of positive integer factors of 42120 that divides 42109 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42109 and 42120. The biggest common factor number is the GCF number.
So the greatest common factor 42109 and 42120 is 1.

Also check out the Least Common Multiple of 42109 and 42120