What is the Greatest Common Factor of 39708 and 39728?

Greatest common factor (GCF) of 39708 and 39728 is 4.

GCF(39708,39728) = 4

We will now calculate the prime factors of 39708 and 39728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39708 and 39728.

How to find the GCF of 39708 and 39728?

We will first find the prime factorization of 39708 and 39728. After we will calculate the factors of 39708 and 39728 and find the biggest common factor number .

Step-1: Prime Factorization of 39708

Prime factors of 39708 are 2, 3, 1103. Prime factorization of 39708 in exponential form is:

39708 = 2² × 3² × 1103¹

Step-2: Prime Factorization of 39728

Prime factors of 39728 are 2, 13, 191. Prime factorization of 39728 in exponential form is:

39728 = 2⁴ × 13¹ × 191¹

Step-3: Factors of 39708

List of positive integer factors of 39708 that divides 39708 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 1103, 2206, 3309, 4412, 6618, 9927, 13236, 19854

Step-4: Factors of 39728

List of positive integer factors of 39728 that divides 39708 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 104, 191, 208, 382, 764, 1528, 2483, 3056, 4966, 9932, 19864

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39708 and 39728. The biggest common factor number is the GCF number.
So the greatest common factor 39708 and 39728 is 4.

Also check out the Least Common Multiple of 39708 and 39728