What is the Greatest Common Factor of 31800 and 31808?

Greatest common factor (GCF) of 31800 and 31808 is 8.

GCF(31800,31808) = 8

We will now calculate the prime factors of 31800 and 31808, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31800 and 31808.

How to find the GCF of 31800 and 31808?

We will first find the prime factorization of 31800 and 31808. After we will calculate the factors of 31800 and 31808 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 31808

Prime factors of 31808 are 2, 7, 71. Prime factorization of 31808 in exponential form is:

31808 = 2⁶ × 7¹ × 71¹

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 31808

List of positive integer factors of 31808 that divides 31800 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 71, 112, 142, 224, 284, 448, 497, 568, 994, 1136, 1988, 2272, 3976, 4544, 7952, 15904

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31800 and 31808. The biggest common factor number is the GCF number.
So the greatest common factor 31800 and 31808 is 8.

Also check out the Least Common Multiple of 31800 and 31808