What is the Greatest Common Factor of 75708 and 75720?

Greatest common factor (GCF) of 75708 and 75720 is 12.

GCF(75708,75720) = 12

We will now calculate the prime factors of 75708 and 75720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75708 and 75720.

How to find the GCF of 75708 and 75720?

We will first find the prime factorization of 75708 and 75720. After we will calculate the factors of 75708 and 75720 and find the biggest common factor number .

Step-1: Prime Factorization of 75708

Prime factors of 75708 are 2, 3, 701. Prime factorization of 75708 in exponential form is:

75708 = 2² × 3³ × 701¹

Step-2: Prime Factorization of 75720

Prime factors of 75720 are 2, 3, 5, 631. Prime factorization of 75720 in exponential form is:

75720 = 2³ × 3¹ × 5¹ × 631¹

Step-3: Factors of 75708

List of positive integer factors of 75708 that divides 75708 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 701, 1402, 2103, 2804, 4206, 6309, 8412, 12618, 18927, 25236, 37854

Step-4: Factors of 75720

List of positive integer factors of 75720 that divides 75708 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 631, 1262, 1893, 2524, 3155, 3786, 5048, 6310, 7572, 9465, 12620, 15144, 18930, 25240, 37860

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75708 and 75720. The biggest common factor number is the GCF number.
So the greatest common factor 75708 and 75720 is 12.

Also check out the Least Common Multiple of 75708 and 75720