What is the Greatest Common Factor of 39300 and 39314?

Greatest common factor (GCF) of 39300 and 39314 is 2.

GCF(39300,39314) = 2

We will now calculate the prime factors of 39300 and 39314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39300 and 39314.

How to find the GCF of 39300 and 39314?

We will first find the prime factorization of 39300 and 39314. After we will calculate the factors of 39300 and 39314 and find the biggest common factor number .

Step-1: Prime Factorization of 39300

Prime factors of 39300 are 2, 3, 5, 131. Prime factorization of 39300 in exponential form is:

39300 = 2² × 3¹ × 5² × 131¹

Step-2: Prime Factorization of 39314

Prime factors of 39314 are 2, 11, 1787. Prime factorization of 39314 in exponential form is:

39314 = 2¹ × 11¹ × 1787¹

Step-3: Factors of 39300

List of positive integer factors of 39300 that divides 39300 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 131, 150, 262, 300, 393, 524, 655, 786, 1310, 1572, 1965, 2620, 3275, 3930, 6550, 7860, 9825, 13100, 19650

Step-4: Factors of 39314

List of positive integer factors of 39314 that divides 39300 without a remainder.

1, 2, 11, 22, 1787, 3574, 19657

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39300 and 39314. The biggest common factor number is the GCF number.
So the greatest common factor 39300 and 39314 is 2.

Also check out the Least Common Multiple of 39300 and 39314