What is the Greatest Common Factor of 30984 and 31000?

Greatest common factor (GCF) of 30984 and 31000 is 8.

GCF(30984,31000) = 8

We will now calculate the prime factors of 30984 and 31000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30984 and 31000.

How to find the GCF of 30984 and 31000?

We will first find the prime factorization of 30984 and 31000. After we will calculate the factors of 30984 and 31000 and find the biggest common factor number .

Step-1: Prime Factorization of 30984

Prime factors of 30984 are 2, 3, 1291. Prime factorization of 30984 in exponential form is:

30984 = 2³ × 3¹ × 1291¹

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 30984

List of positive integer factors of 30984 that divides 30984 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 1291, 2582, 3873, 5164, 7746, 10328, 15492

Step-4: Factors of 31000

List of positive integer factors of 31000 that divides 30984 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 30984 and 31000. The biggest common factor number is the GCF number.
So the greatest common factor 30984 and 31000 is 8.

Also check out the Least Common Multiple of 30984 and 31000