What is the Greatest Common Factor of 31890 and 31900?

Greatest common factor (GCF) of 31890 and 31900 is 10.

GCF(31890,31900) = 10

We will now calculate the prime factors of 31890 and 31900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31890 and 31900.

How to find the GCF of 31890 and 31900?

We will first find the prime factorization of 31890 and 31900. After we will calculate the factors of 31890 and 31900 and find the biggest common factor number .

Step-1: Prime Factorization of 31890

Prime factors of 31890 are 2, 3, 5, 1063. Prime factorization of 31890 in exponential form is:

31890 = 2¹ × 3¹ × 5¹ × 1063¹

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 31890

List of positive integer factors of 31890 that divides 31890 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 1063, 2126, 3189, 5315, 6378, 10630, 15945

Step-4: Factors of 31900

List of positive integer factors of 31900 that divides 31890 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 31890 and 31900. The biggest common factor number is the GCF number.
So the greatest common factor 31890 and 31900 is 10.

Also check out the Least Common Multiple of 31890 and 31900