What is the Greatest Common Factor of 31005 and 31023?

Greatest common factor (GCF) of 31005 and 31023 is 9.

GCF(31005,31023) = 9

We will now calculate the prime factors of 31005 and 31023, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31005 and 31023.

How to find the GCF of 31005 and 31023?

We will first find the prime factorization of 31005 and 31023. After we will calculate the factors of 31005 and 31023 and find the biggest common factor number .

Step-1: Prime Factorization of 31005

Prime factors of 31005 are 3, 5, 13, 53. Prime factorization of 31005 in exponential form is:

31005 = 3² × 5¹ × 13¹ × 53¹

Step-2: Prime Factorization of 31023

Prime factors of 31023 are 3, 383. Prime factorization of 31023 in exponential form is:

31023 = 3⁴ × 383¹

Step-3: Factors of 31005

List of positive integer factors of 31005 that divides 31005 without a remainder.

1, 3, 5, 9, 13, 15, 39, 45, 53, 65, 117, 159, 195, 265, 477, 585, 689, 795, 2067, 2385, 3445, 6201, 10335

Step-4: Factors of 31023

List of positive integer factors of 31023 that divides 31005 without a remainder.

1, 3, 9, 27, 81, 383, 1149, 3447, 10341

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31005 and 31023. The biggest common factor number is the GCF number.
So the greatest common factor 31005 and 31023 is 9.

Also check out the Least Common Multiple of 31005 and 31023