What is the Greatest Common Factor of 31704 and 31724?

Greatest common factor (GCF) of 31704 and 31724 is 4.

GCF(31704,31724) = 4

We will now calculate the prime factors of 31704 and 31724, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31704 and 31724.

How to find the GCF of 31704 and 31724?

We will first find the prime factorization of 31704 and 31724. After we will calculate the factors of 31704 and 31724 and find the biggest common factor number .

Step-1: Prime Factorization of 31704

Prime factors of 31704 are 2, 3, 1321. Prime factorization of 31704 in exponential form is:

31704 = 2³ × 3¹ × 1321¹

Step-2: 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-3: Factors of 31704

List of positive integer factors of 31704 that divides 31704 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 1321, 2642, 3963, 5284, 7926, 10568, 15852

Step-4: Factors of 31724

List of positive integer factors of 31724 that divides 31704 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31704 and 31724. The biggest common factor number is the GCF number.
So the greatest common factor 31704 and 31724 is 4.

Also check out the Least Common Multiple of 31704 and 31724