What is the Greatest Common Factor of 39888 and 39900?

Greatest common factor (GCF) of 39888 and 39900 is 12.

GCF(39888,39900) = 12

We will now calculate the prime factors of 39888 and 39900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39888 and 39900.

How to find the GCF of 39888 and 39900?

We will first find the prime factorization of 39888 and 39900. After we will calculate the factors of 39888 and 39900 and find the biggest common factor number .

Step-1: Prime Factorization of 39888

Prime factors of 39888 are 2, 3, 277. Prime factorization of 39888 in exponential form is:

39888 = 2⁴ × 3² × 277¹

Step-2: 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-3: Factors of 39888

List of positive integer factors of 39888 that divides 39888 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 277, 554, 831, 1108, 1662, 2216, 2493, 3324, 4432, 4986, 6648, 9972, 13296, 19944

Step-4: Factors of 39900

List of positive integer factors of 39900 that divides 39888 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39888 and 39900. The biggest common factor number is the GCF number.
So the greatest common factor 39888 and 39900 is 12.

Also check out the Least Common Multiple of 39888 and 39900