What is the Greatest Common Factor of 31808 and 31822?

Greatest common factor (GCF) of 31808 and 31822 is 14.

GCF(31808,31822) = 14

We will now calculate the prime factors of 31808 and 31822, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31808 and 31822.

How to find the GCF of 31808 and 31822?

We will first find the prime factorization of 31808 and 31822. After we will calculate the factors of 31808 and 31822 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31822

Prime factors of 31822 are 2, 7, 2273. Prime factorization of 31822 in exponential form is:

31822 = 2¹ × 7¹ × 2273¹

Step-3: Factors of 31808

List of positive integer factors of 31808 that divides 31808 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

Step-4: Factors of 31822

List of positive integer factors of 31822 that divides 31808 without a remainder.

1, 2, 7, 14, 2273, 4546, 15911

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31808 and 31822. The biggest common factor number is the GCF number.
So the greatest common factor 31808 and 31822 is 14.

Also check out the Least Common Multiple of 31808 and 31822