What is the Greatest Common Factor of 31605 and 31609?

Greatest common factor (GCF) of 31605 and 31609 is 1.

GCF(31605,31609) = 1

We will now calculate the prime factors of 31605 and 31609, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31605 and 31609.

How to find the GCF of 31605 and 31609?

We will first find the prime factorization of 31605 and 31609. After we will calculate the factors of 31605 and 31609 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31609

Prime factors of 31609 are 73, 433. Prime factorization of 31609 in exponential form is:

31609 = 73¹ × 433¹

Step-3: Factors of 31605

List of positive integer factors of 31605 that divides 31605 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

Step-4: Factors of 31609

List of positive integer factors of 31609 that divides 31605 without a remainder.

1, 73, 433

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31605 and 31609. The biggest common factor number is the GCF number.
So the greatest common factor 31605 and 31609 is 1.

Also check out the Least Common Multiple of 31605 and 31609