What is the Greatest Common Factor of 39900 and 39920?

Greatest common factor (GCF) of 39900 and 39920 is 20.

GCF(39900,39920) = 20

We will now calculate the prime factors of 39900 and 39920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39900 and 39920.

How to find the GCF of 39900 and 39920?

We will first find the prime factorization of 39900 and 39920. After we will calculate the factors of 39900 and 39920 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 39920

Prime factors of 39920 are 2, 5, 499. Prime factorization of 39920 in exponential form is:

39920 = 2⁴ × 5¹ × 499¹

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 39920

List of positive integer factors of 39920 that divides 39900 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 499, 998, 1996, 2495, 3992, 4990, 7984, 9980, 19960

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39900 and 39920. The biggest common factor number is the GCF number.
So the greatest common factor 39900 and 39920 is 20.

Also check out the Least Common Multiple of 39900 and 39920