What is the Greatest Common Factor of 30986 and 31000?

Greatest common factor (GCF) of 30986 and 31000 is 2.

GCF(30986,31000) = 2

We will now calculate the prime factors of 30986 and 31000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30986 and 31000.

How to find the GCF of 30986 and 31000?

We will first find the prime factorization of 30986 and 31000. After we will calculate the factors of 30986 and 31000 and find the biggest common factor number .

Step-1: Prime Factorization of 30986

Prime factors of 30986 are 2, 15493. Prime factorization of 30986 in exponential form is:

30986 = 2¹ × 15493¹

Step-2: 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-3: Factors of 30986

List of positive integer factors of 30986 that divides 30986 without a remainder.

1, 2, 15493

Step-4: Factors of 31000

List of positive integer factors of 31000 that divides 30986 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30986 and 31000. The biggest common factor number is the GCF number.
So the greatest common factor 30986 and 31000 is 2.

Also check out the Least Common Multiple of 30986 and 31000