What is the Greatest Common Factor of 39294 and 39300?

Greatest common factor (GCF) of 39294 and 39300 is 6.

GCF(39294,39300) = 6

We will now calculate the prime factors of 39294 and 39300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39294 and 39300.

How to find the GCF of 39294 and 39300?

We will first find the prime factorization of 39294 and 39300. After we will calculate the factors of 39294 and 39300 and find the biggest common factor number .

Step-1: Prime Factorization of 39294

Prime factors of 39294 are 2, 3, 37, 59. Prime factorization of 39294 in exponential form is:

39294 = 2¹ × 3² × 37¹ × 59¹

Step-2: 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-3: Factors of 39294

List of positive integer factors of 39294 that divides 39294 without a remainder.

1, 2, 3, 6, 9, 18, 37, 59, 74, 111, 118, 177, 222, 333, 354, 531, 666, 1062, 2183, 4366, 6549, 13098, 19647

Step-4: Factors of 39300

List of positive integer factors of 39300 that divides 39294 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39294 and 39300. The biggest common factor number is the GCF number.
So the greatest common factor 39294 and 39300 is 6.

Also check out the Least Common Multiple of 39294 and 39300