What is the Greatest Common Factor of 31785 and 31800?

Greatest common factor (GCF) of 31785 and 31800 is 15.

GCF(31785,31800) = 15

We will now calculate the prime factors of 31785 and 31800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31785 and 31800.

How to find the GCF of 31785 and 31800?

We will first find the prime factorization of 31785 and 31800. After we will calculate the factors of 31785 and 31800 and find the biggest common factor number .

Step-1: Prime Factorization of 31785

Prime factors of 31785 are 3, 5, 13, 163. Prime factorization of 31785 in exponential form is:

31785 = 3¹ × 5¹ × 13¹ × 163¹

Step-2: 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-3: Factors of 31785

List of positive integer factors of 31785 that divides 31785 without a remainder.

1, 3, 5, 13, 15, 39, 65, 163, 195, 489, 815, 2119, 2445, 6357, 10595

Step-4: Factors of 31800

List of positive integer factors of 31800 that divides 31785 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31785 and 31800. The biggest common factor number is the GCF number.
So the greatest common factor 31785 and 31800 is 15.

Also check out the Least Common Multiple of 31785 and 31800