What is the Greatest Common Factor of 31682 and 31689?

Greatest common factor (GCF) of 31682 and 31689 is 7.

GCF(31682,31689) = 7

We will now calculate the prime factors of 31682 and 31689, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31682 and 31689.

How to find the GCF of 31682 and 31689?

We will first find the prime factorization of 31682 and 31689. After we will calculate the factors of 31682 and 31689 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31689

Prime factors of 31689 are 3, 7, 503. Prime factorization of 31689 in exponential form is:

31689 = 3² × 7¹ × 503¹

Step-3: Factors of 31682

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

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

Step-4: Factors of 31689

List of positive integer factors of 31689 that divides 31682 without a remainder.

1, 3, 7, 9, 21, 63, 503, 1509, 3521, 4527, 10563

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31682 and 31689. The biggest common factor number is the GCF number.
So the greatest common factor 31682 and 31689 is 7.

Also check out the Least Common Multiple of 31682 and 31689