What is the Greatest Common Factor of 42300 and 42314?

Greatest common factor (GCF) of 42300 and 42314 is 2.

GCF(42300,42314) = 2

We will now calculate the prime factors of 42300 and 42314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42300 and 42314.

How to find the GCF of 42300 and 42314?

We will first find the prime factorization of 42300 and 42314. After we will calculate the factors of 42300 and 42314 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 42314

Prime factors of 42314 are 2, 21157. Prime factorization of 42314 in exponential form is:

42314 = 2¹ × 21157¹

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 42314

List of positive integer factors of 42314 that divides 42300 without a remainder.

1, 2, 21157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42300 and 42314. The biggest common factor number is the GCF number.
So the greatest common factor 42300 and 42314 is 2.

Also check out the Least Common Multiple of 42300 and 42314