What is the Greatest Common Factor of 31724 and 31735?

Greatest common factor (GCF) of 31724 and 31735 is 11.

GCF(31724,31735) = 11

We will now calculate the prime factors of 31724 and 31735, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31724 and 31735.

How to find the GCF of 31724 and 31735?

We will first find the prime factorization of 31724 and 31735. After we will calculate the factors of 31724 and 31735 and find the biggest common factor number .

Step-1: Prime Factorization of 31724

Prime factors of 31724 are 2, 7, 11, 103. Prime factorization of 31724 in exponential form is:

31724 = 2² × 7¹ × 11¹ × 103¹

Step-2: Prime Factorization of 31735

Prime factors of 31735 are 5, 11, 577. Prime factorization of 31735 in exponential form is:

31735 = 5¹ × 11¹ × 577¹

Step-3: Factors of 31724

List of positive integer factors of 31724 that divides 31724 without a remainder.

1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 103, 154, 206, 308, 412, 721, 1133, 1442, 2266, 2884, 4532, 7931, 15862

Step-4: Factors of 31735

List of positive integer factors of 31735 that divides 31724 without a remainder.

1, 5, 11, 55, 577, 2885, 6347

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31724 and 31735. The biggest common factor number is the GCF number.
So the greatest common factor 31724 and 31735 is 11.

Also check out the Least Common Multiple of 31724 and 31735