What is the Greatest Common Factor of 31591 and 31605?

Greatest common factor (GCF) of 31591 and 31605 is 7.

GCF(31591,31605) = 7

We will now calculate the prime factors of 31591 and 31605, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31591 and 31605.

How to find the GCF of 31591 and 31605?

We will first find the prime factorization of 31591 and 31605. After we will calculate the factors of 31591 and 31605 and find the biggest common factor number .

Step-1: Prime Factorization of 31591

Prime factors of 31591 are 7, 4513. Prime factorization of 31591 in exponential form is:

31591 = 7¹ × 4513¹

Step-2: Prime Factorization of 31605

Prime factors of 31605 are 3, 5, 7, 43. Prime factorization of 31605 in exponential form is:

31605 = 3¹ × 5¹ × 7² × 43¹

Step-3: Factors of 31591

List of positive integer factors of 31591 that divides 31591 without a remainder.

1, 7, 4513

Step-4: Factors of 31605

List of positive integer factors of 31605 that divides 31591 without a remainder.

1, 3, 5, 7, 15, 21, 35, 43, 49, 105, 129, 147, 215, 245, 301, 645, 735, 903, 1505, 2107, 4515, 6321, 10535

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31591 and 31605. The biggest common factor number is the GCF number.
So the greatest common factor 31591 and 31605 is 7.

Also check out the Least Common Multiple of 31591 and 31605