What is the Greatest Common Factor of 31000 and 31009?

Greatest common factor (GCF) of 31000 and 31009 is 1.

GCF(31000,31009) = 1

We will now calculate the prime factors of 31000 and 31009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31000 and 31009.

How to find the GCF of 31000 and 31009?

We will first find the prime factorization of 31000 and 31009. After we will calculate the factors of 31000 and 31009 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 31009

Prime factors of 31009 are 11, 2819. Prime factorization of 31009 in exponential form is:

31009 = 11¹ × 2819¹

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 31009

List of positive integer factors of 31009 that divides 31000 without a remainder.

1, 11, 2819

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31000 and 31009. The biggest common factor number is the GCF number.
So the greatest common factor 31000 and 31009 is 1.

Also check out the Least Common Multiple of 31000 and 31009