What is the Greatest Common Factor of 39900 and 39914?

Greatest common factor (GCF) of 39900 and 39914 is 14.

GCF(39900,39914) = 14

We will now calculate the prime factors of 39900 and 39914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39900 and 39914.

How to find the GCF of 39900 and 39914?

We will first find the prime factorization of 39900 and 39914. After we will calculate the factors of 39900 and 39914 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 39914

Prime factors of 39914 are 2, 7, 2851. Prime factorization of 39914 in exponential form is:

39914 = 2¹ × 7¹ × 2851¹

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 39914

List of positive integer factors of 39914 that divides 39900 without a remainder.

1, 2, 7, 14, 2851, 5702, 19957

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39900 and 39914. The biggest common factor number is the GCF number.
So the greatest common factor 39900 and 39914 is 14.

Also check out the Least Common Multiple of 39900 and 39914