What is the Greatest Common Factor of 31884 and 31900?

Greatest common factor (GCF) of 31884 and 31900 is 4.

GCF(31884,31900) = 4

We will now calculate the prime factors of 31884 and 31900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31884 and 31900.

How to find the GCF of 31884 and 31900?

We will first find the prime factorization of 31884 and 31900. After we will calculate the factors of 31884 and 31900 and find the biggest common factor number .

Step-1: Prime Factorization of 31884

Prime factors of 31884 are 2, 3, 2657. Prime factorization of 31884 in exponential form is:

31884 = 2² × 3¹ × 2657¹

Step-2: Prime Factorization of 31900

Prime factors of 31900 are 2, 5, 11, 29. Prime factorization of 31900 in exponential form is:

31900 = 2² × 5² × 11¹ × 29¹

Step-3: Factors of 31884

List of positive integer factors of 31884 that divides 31884 without a remainder.

1, 2, 3, 4, 6, 12, 2657, 5314, 7971, 10628, 15942

Step-4: Factors of 31900

List of positive integer factors of 31900 that divides 31884 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 25, 29, 44, 50, 55, 58, 100, 110, 116, 145, 220, 275, 290, 319, 550, 580, 638, 725, 1100, 1276, 1450, 1595, 2900, 3190, 6380, 7975, 15950

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31884 and 31900. The biggest common factor number is the GCF number.
So the greatest common factor 31884 and 31900 is 4.

Also check out the Least Common Multiple of 31884 and 31900