What is the Greatest Common Factor of 31664 and 31682?

Greatest common factor (GCF) of 31664 and 31682 is 2.

GCF(31664,31682) = 2

We will now calculate the prime factors of 31664 and 31682, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31664 and 31682.

How to find the GCF of 31664 and 31682?

We will first find the prime factorization of 31664 and 31682. After we will calculate the factors of 31664 and 31682 and find the biggest common factor number .

Step-1: Prime Factorization of 31664

Prime factors of 31664 are 2, 1979. Prime factorization of 31664 in exponential form is:

31664 = 2⁴ × 1979¹

Step-2: Prime Factorization of 31682

Prime factors of 31682 are 2, 7, 31, 73. Prime factorization of 31682 in exponential form is:

31682 = 2¹ × 7¹ × 31¹ × 73¹

Step-3: Factors of 31664

List of positive integer factors of 31664 that divides 31664 without a remainder.

1, 2, 4, 8, 16, 1979, 3958, 7916, 15832

Step-4: Factors of 31682

List of positive integer factors of 31682 that divides 31664 without a remainder.

1, 2, 7, 14, 31, 62, 73, 146, 217, 434, 511, 1022, 2263, 4526, 15841

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31664 and 31682. The biggest common factor number is the GCF number.
So the greatest common factor 31664 and 31682 is 2.

Also check out the Least Common Multiple of 31664 and 31682