What is the Greatest Common Factor of 31408 and 31424?

Greatest common factor (GCF) of 31408 and 31424 is 16.

GCF(31408,31424) = 16

We will now calculate the prime factors of 31408 and 31424, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31408 and 31424.

How to find the GCF of 31408 and 31424?

We will first find the prime factorization of 31408 and 31424. After we will calculate the factors of 31408 and 31424 and find the biggest common factor number .

Step-1: Prime Factorization of 31408

Prime factors of 31408 are 2, 13, 151. Prime factorization of 31408 in exponential form is:

31408 = 2⁴ × 13¹ × 151¹

Step-2: Prime Factorization of 31424

Prime factors of 31424 are 2, 491. Prime factorization of 31424 in exponential form is:

31424 = 2⁶ × 491¹

Step-3: Factors of 31408

List of positive integer factors of 31408 that divides 31408 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 104, 151, 208, 302, 604, 1208, 1963, 2416, 3926, 7852, 15704

Step-4: Factors of 31424

List of positive integer factors of 31424 that divides 31408 without a remainder.

1, 2, 4, 8, 16, 32, 64, 491, 982, 1964, 3928, 7856, 15712

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31408 and 31424. The biggest common factor number is the GCF number.
So the greatest common factor 31408 and 31424 is 16.

Also check out the Least Common Multiple of 31408 and 31424