What is the Greatest Common Factor of 39892 and 39900?

Greatest common factor (GCF) of 39892 and 39900 is 4.

GCF(39892,39900) = 4

We will now calculate the prime factors of 39892 and 39900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39892 and 39900.

How to find the GCF of 39892 and 39900?

We will first find the prime factorization of 39892 and 39900. After we will calculate the factors of 39892 and 39900 and find the biggest common factor number .

Step-1: Prime Factorization of 39892

Prime factors of 39892 are 2, 9973. Prime factorization of 39892 in exponential form is:

39892 = 2² × 9973¹

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 39892

List of positive integer factors of 39892 that divides 39892 without a remainder.

1, 2, 4, 9973, 19946

Step-4: Factors of 39900

List of positive integer factors of 39900 that divides 39892 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 39892 and 39900. The biggest common factor number is the GCF number.
So the greatest common factor 39892 and 39900 is 4.

Also check out the Least Common Multiple of 39892 and 39900