What is the Greatest Common Factor of 42285 and 42300?

Greatest common factor (GCF) of 42285 and 42300 is 15.

GCF(42285,42300) = 15

We will now calculate the prime factors of 42285 and 42300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42285 and 42300.

How to find the GCF of 42285 and 42300?

We will first find the prime factorization of 42285 and 42300. After we will calculate the factors of 42285 and 42300 and find the biggest common factor number .

Step-1: Prime Factorization of 42285

Prime factors of 42285 are 3, 5, 2819. Prime factorization of 42285 in exponential form is:

42285 = 3¹ × 5¹ × 2819¹

Step-2: Prime Factorization of 42300

Prime factors of 42300 are 2, 3, 5, 47. Prime factorization of 42300 in exponential form is:

42300 = 2² × 3² × 5² × 47¹

Step-3: Factors of 42285

List of positive integer factors of 42285 that divides 42285 without a remainder.

1, 3, 5, 15, 2819, 8457, 14095

Step-4: Factors of 42300

List of positive integer factors of 42300 that divides 42285 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 47, 50, 60, 75, 90, 94, 100, 141, 150, 180, 188, 225, 235, 282, 300, 423, 450, 470, 564, 705, 846, 900, 940, 1175, 1410, 1692, 2115, 2350, 2820, 3525, 4230, 4700, 7050, 8460, 10575, 14100, 21150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42285 and 42300. The biggest common factor number is the GCF number.
So the greatest common factor 42285 and 42300 is 15.

Also check out the Least Common Multiple of 42285 and 42300