What is the Greatest Common Factor of 31722 and 31739?

Greatest common factor (GCF) of 31722 and 31739 is 17.

GCF(31722,31739) = 17

We will now calculate the prime factors of 31722 and 31739, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31722 and 31739.

How to find the GCF of 31722 and 31739?

We will first find the prime factorization of 31722 and 31739. After we will calculate the factors of 31722 and 31739 and find the biggest common factor number .

Step-1: Prime Factorization of 31722

Prime factors of 31722 are 2, 3, 17, 311. Prime factorization of 31722 in exponential form is:

31722 = 2¹ × 3¹ × 17¹ × 311¹

Step-2: Prime Factorization of 31739

Prime factors of 31739 are 17, 1867. Prime factorization of 31739 in exponential form is:

31739 = 17¹ × 1867¹

Step-3: Factors of 31722

List of positive integer factors of 31722 that divides 31722 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 311, 622, 933, 1866, 5287, 10574, 15861

Step-4: Factors of 31739

List of positive integer factors of 31739 that divides 31722 without a remainder.

1, 17, 1867

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31722 and 31739. The biggest common factor number is the GCF number.
So the greatest common factor 31722 and 31739 is 17.

Also check out the Least Common Multiple of 31722 and 31739