What is the Greatest Common Factor of 31800 and 31810?

Greatest common factor (GCF) of 31800 and 31810 is 10.

GCF(31800,31810) = 10

We will now calculate the prime factors of 31800 and 31810, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31800 and 31810.

How to find the GCF of 31800 and 31810?

We will first find the prime factorization of 31800 and 31810. After we will calculate the factors of 31800 and 31810 and find the biggest common factor number .

Step-1: Prime Factorization of 31800

Prime factors of 31800 are 2, 3, 5, 53. Prime factorization of 31800 in exponential form is:

31800 = 2³ × 3¹ × 5² × 53¹

Step-2: Prime Factorization of 31810

Prime factors of 31810 are 2, 5, 3181. Prime factorization of 31810 in exponential form is:

31810 = 2¹ × 5¹ × 3181¹

Step-3: Factors of 31800

List of positive integer factors of 31800 that divides 31800 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 53, 60, 75, 100, 106, 120, 150, 159, 200, 212, 265, 300, 318, 424, 530, 600, 636, 795, 1060, 1272, 1325, 1590, 2120, 2650, 3180, 3975, 5300, 6360, 7950, 10600, 15900

Step-4: Factors of 31810

List of positive integer factors of 31810 that divides 31800 without a remainder.

1, 2, 5, 10, 3181, 6362, 15905

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31800 and 31810. The biggest common factor number is the GCF number.
So the greatest common factor 31800 and 31810 is 10.

Also check out the Least Common Multiple of 31800 and 31810