What is the Greatest Common Factor of 39900 and 39904?

Greatest common factor (GCF) of 39900 and 39904 is 4.

GCF(39900,39904) = 4

We will now calculate the prime factors of 39900 and 39904, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39900 and 39904.

How to find the GCF of 39900 and 39904?

We will first find the prime factorization of 39900 and 39904. After we will calculate the factors of 39900 and 39904 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 39904

Prime factors of 39904 are 2, 29, 43. Prime factorization of 39904 in exponential form is:

39904 = 2⁵ × 29¹ × 43¹

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 39904

List of positive integer factors of 39904 that divides 39900 without a remainder.

1, 2, 4, 8, 16, 29, 32, 43, 58, 86, 116, 172, 232, 344, 464, 688, 928, 1247, 1376, 2494, 4988, 9976, 19952

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39900 and 39904. The biggest common factor number is the GCF number.
So the greatest common factor 39900 and 39904 is 4.

Also check out the Least Common Multiple of 39900 and 39904