What is the Greatest Common Factor of 31786 and 31800?

Greatest common factor (GCF) of 31786 and 31800 is 2.

GCF(31786,31800) = 2

We will now calculate the prime factors of 31786 and 31800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31786 and 31800.

How to find the GCF of 31786 and 31800?

We will first find the prime factorization of 31786 and 31800. After we will calculate the factors of 31786 and 31800 and find the biggest common factor number .

Step-1: Prime Factorization of 31786

Prime factors of 31786 are 2, 23, 691. Prime factorization of 31786 in exponential form is:

31786 = 2¹ × 23¹ × 691¹

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 31786

List of positive integer factors of 31786 that divides 31786 without a remainder.

1, 2, 23, 46, 691, 1382, 15893

Step-4: Factors of 31800

List of positive integer factors of 31800 that divides 31786 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 31786 and 31800. The biggest common factor number is the GCF number.
So the greatest common factor 31786 and 31800 is 2.

Also check out the Least Common Multiple of 31786 and 31800