What is the Greatest Common Factor of 42405 and 42420?

Greatest common factor (GCF) of 42405 and 42420 is 15.

GCF(42405,42420) = 15

We will now calculate the prime factors of 42405 and 42420, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42405 and 42420.

How to find the GCF of 42405 and 42420?

We will first find the prime factorization of 42405 and 42420. After we will calculate the factors of 42405 and 42420 and find the biggest common factor number .

Step-1: Prime Factorization of 42405

Prime factors of 42405 are 3, 5, 11, 257. Prime factorization of 42405 in exponential form is:

42405 = 3¹ × 5¹ × 11¹ × 257¹

Step-2: Prime Factorization of 42420

Prime factors of 42420 are 2, 3, 5, 7, 101. Prime factorization of 42420 in exponential form is:

42420 = 2² × 3¹ × 5¹ × 7¹ × 101¹

Step-3: Factors of 42405

List of positive integer factors of 42405 that divides 42405 without a remainder.

1, 3, 5, 11, 15, 33, 55, 165, 257, 771, 1285, 2827, 3855, 8481, 14135

Step-4: Factors of 42420

List of positive integer factors of 42420 that divides 42405 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 101, 105, 140, 202, 210, 303, 404, 420, 505, 606, 707, 1010, 1212, 1414, 1515, 2020, 2121, 2828, 3030, 3535, 4242, 6060, 7070, 8484, 10605, 14140, 21210

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42405 and 42420. The biggest common factor number is the GCF number.
So the greatest common factor 42405 and 42420 is 15.

Also check out the Least Common Multiple of 42405 and 42420