What is the Greatest Common Factor of 31000 and 31005?

Greatest common factor (GCF) of 31000 and 31005 is 5.

GCF(31000,31005) = 5

We will now calculate the prime factors of 31000 and 31005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31000 and 31005.

How to find the GCF of 31000 and 31005?

We will first find the prime factorization of 31000 and 31005. After we will calculate the factors of 31000 and 31005 and find the biggest common factor number .

Step-1: Prime Factorization of 31000

Prime factors of 31000 are 2, 5, 31. Prime factorization of 31000 in exponential form is:

31000 = 2³ × 5³ × 31¹

Step-2: 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-3: Factors of 31000

List of positive integer factors of 31000 that divides 31000 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 31, 40, 50, 62, 100, 124, 125, 155, 200, 248, 250, 310, 500, 620, 775, 1000, 1240, 1550, 3100, 3875, 6200, 7750, 15500

Step-4: Factors of 31005

List of positive integer factors of 31005 that divides 31000 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31000 and 31005. The biggest common factor number is the GCF number.
So the greatest common factor 31000 and 31005 is 5.

Also check out the Least Common Multiple of 31000 and 31005