What is the Greatest Common Factor of 39960 and 39974?

Greatest common factor (GCF) of 39960 and 39974 is 2.

GCF(39960,39974) = 2

We will now calculate the prime factors of 39960 and 39974, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39960 and 39974.

How to find the GCF of 39960 and 39974?

We will first find the prime factorization of 39960 and 39974. After we will calculate the factors of 39960 and 39974 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 39974

Prime factors of 39974 are 2, 11, 23, 79. Prime factorization of 39974 in exponential form is:

39974 = 2¹ × 11¹ × 23¹ × 79¹

Step-3: Factors of 39960

List of positive integer factors of 39960 that divides 39960 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

Step-4: Factors of 39974

List of positive integer factors of 39974 that divides 39960 without a remainder.

1, 2, 11, 22, 23, 46, 79, 158, 253, 506, 869, 1738, 1817, 3634, 19987

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39960 and 39974. The biggest common factor number is the GCF number.
So the greatest common factor 39960 and 39974 is 2.

Also check out the Least Common Multiple of 39960 and 39974