What is the Greatest Common Factor of 42105 and 42120?

Greatest common factor (GCF) of 42105 and 42120 is 15.

GCF(42105,42120) = 15

We will now calculate the prime factors of 42105 and 42120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42105 and 42120.

How to find the GCF of 42105 and 42120?

We will first find the prime factorization of 42105 and 42120. After we will calculate the factors of 42105 and 42120 and find the biggest common factor number .

Step-1: Prime Factorization of 42105

Prime factors of 42105 are 3, 5, 7, 401. Prime factorization of 42105 in exponential form is:

42105 = 3¹ × 5¹ × 7¹ × 401¹

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 42105

List of positive integer factors of 42105 that divides 42105 without a remainder.

1, 3, 5, 7, 15, 21, 35, 105, 401, 1203, 2005, 2807, 6015, 8421, 14035

Step-4: Factors of 42120

List of positive integer factors of 42120 that divides 42105 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 42105 and 42120. The biggest common factor number is the GCF number.
So the greatest common factor 42105 and 42120 is 15.

Also check out the Least Common Multiple of 42105 and 42120