What is the Greatest Common Factor of 31005 and 31020?

Greatest common factor (GCF) of 31005 and 31020 is 15.

GCF(31005,31020) = 15

We will now calculate the prime factors of 31005 and 31020, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31005 and 31020.

How to find the GCF of 31005 and 31020?

We will first find the prime factorization of 31005 and 31020. After we will calculate the factors of 31005 and 31020 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 31020

Prime factors of 31020 are 2, 3, 5, 11, 47. Prime factorization of 31020 in exponential form is:

31020 = 2² × 3¹ × 5¹ × 11¹ × 47¹

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 31020

List of positive integer factors of 31020 that divides 31005 without a remainder.

1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 47, 55, 60, 66, 94, 110, 132, 141, 165, 188, 220, 235, 282, 330, 470, 517, 564, 660, 705, 940, 1034, 1410, 1551, 2068, 2585, 2820, 3102, 5170, 6204, 7755, 10340, 15510

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31005 and 31020. The biggest common factor number is the GCF number.
So the greatest common factor 31005 and 31020 is 15.

Also check out the Least Common Multiple of 31005 and 31020