What is the Greatest Common Factor of 39900 and 39912?

Greatest common factor (GCF) of 39900 and 39912 is 12.

GCF(39900,39912) = 12

We will now calculate the prime factors of 39900 and 39912, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39900 and 39912.

How to find the GCF of 39900 and 39912?

We will first find the prime factorization of 39900 and 39912. After we will calculate the factors of 39900 and 39912 and find the biggest common factor number .

Step-1: Prime Factorization of 39900

Prime factors of 39900 are 2, 3, 5, 7, 19. Prime factorization of 39900 in exponential form is:

39900 = 2² × 3¹ × 5² × 7¹ × 19¹

Step-2: Prime Factorization of 39912

Prime factors of 39912 are 2, 3, 1663. Prime factorization of 39912 in exponential form is:

39912 = 2³ × 3¹ × 1663¹

Step-3: Factors of 39900

List of positive integer factors of 39900 that divides 39900 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 19, 20, 21, 25, 28, 30, 35, 38, 42, 50, 57, 60, 70, 75, 76, 84, 95, 100, 105, 114, 133, 140, 150, 175, 190, 210, 228, 266, 285, 300, 350, 380, 399, 420, 475, 525, 532, 570, 665, 700, 798, 950, 1050, 1140, 1330, 1425, 1596, 1900, 1995, 2100, 2660, 2850, 3325, 3990, 5700, 6650, 7980, 9975, 13300, 19950

Step-4: Factors of 39912

List of positive integer factors of 39912 that divides 39900 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 1663, 3326, 4989, 6652, 9978, 13304, 19956

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39900 and 39912. The biggest common factor number is the GCF number.
So the greatest common factor 39900 and 39912 is 12.

Also check out the Least Common Multiple of 39900 and 39912