What is the Greatest Common Factor of 39924 and 39942?

Greatest common factor (GCF) of 39924 and 39942 is 18.

GCF(39924,39942) = 18

We will now calculate the prime factors of 39924 and 39942, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39924 and 39942.

How to find the GCF of 39924 and 39942?

We will first find the prime factorization of 39924 and 39942. After we will calculate the factors of 39924 and 39942 and find the biggest common factor number .

Step-1: Prime Factorization of 39924

Prime factors of 39924 are 2, 3, 1109. Prime factorization of 39924 in exponential form is:

39924 = 2² × 3² × 1109¹

Step-2: Prime Factorization of 39942

Prime factors of 39942 are 2, 3, 7, 317. Prime factorization of 39942 in exponential form is:

39942 = 2¹ × 3² × 7¹ × 317¹

Step-3: Factors of 39924

List of positive integer factors of 39924 that divides 39924 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 1109, 2218, 3327, 4436, 6654, 9981, 13308, 19962

Step-4: Factors of 39942

List of positive integer factors of 39942 that divides 39924 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 317, 634, 951, 1902, 2219, 2853, 4438, 5706, 6657, 13314, 19971

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39924 and 39942. The biggest common factor number is the GCF number.
So the greatest common factor 39924 and 39942 is 18.

Also check out the Least Common Multiple of 39924 and 39942