What is the Greatest Common Factor of 42300 and 42320?

Greatest common factor (GCF) of 42300 and 42320 is 20.

GCF(42300,42320) = 20

We will now calculate the prime factors of 42300 and 42320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42300 and 42320.

How to find the GCF of 42300 and 42320?

We will first find the prime factorization of 42300 and 42320. After we will calculate the factors of 42300 and 42320 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 42320

Prime factors of 42320 are 2, 5, 23. Prime factorization of 42320 in exponential form is:

42320 = 2⁴ × 5¹ × 23²

Step-3: Factors of 42300

List of positive integer factors of 42300 that divides 42300 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

Step-4: Factors of 42320

List of positive integer factors of 42320 that divides 42300 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 23, 40, 46, 80, 92, 115, 184, 230, 368, 460, 529, 920, 1058, 1840, 2116, 2645, 4232, 5290, 8464, 10580, 21160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42300 and 42320. The biggest common factor number is the GCF number.
So the greatest common factor 42300 and 42320 is 20.

Also check out the Least Common Multiple of 42300 and 42320