What is the Greatest Common Factor of 39942 and 39960?

Greatest common factor (GCF) of 39942 and 39960 is 18.

GCF(39942,39960) = 18

We will now calculate the prime factors of 39942 and 39960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39942 and 39960.

How to find the GCF of 39942 and 39960?

We will first find the prime factorization of 39942 and 39960. After we will calculate the factors of 39942 and 39960 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 39960

Prime factors of 39960 are 2, 3, 5, 37. Prime factorization of 39960 in exponential form is:

39960 = 2³ × 3³ × 5¹ × 37¹

Step-3: Factors of 39942

List of positive integer factors of 39942 that divides 39942 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

Step-4: Factors of 39960

List of positive integer factors of 39960 that divides 39942 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 37, 40, 45, 54, 60, 72, 74, 90, 108, 111, 120, 135, 148, 180, 185, 216, 222, 270, 296, 333, 360, 370, 444, 540, 555, 666, 740, 888, 999, 1080, 1110, 1332, 1480, 1665, 1998, 2220, 2664, 3330, 3996, 4440, 4995, 6660, 7992, 9990, 13320, 19980

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39942 and 39960. The biggest common factor number is the GCF number.
So the greatest common factor 39942 and 39960 is 18.

Also check out the Least Common Multiple of 39942 and 39960