What is the Greatest Common Factor of 31509 and 31520?

Greatest common factor (GCF) of 31509 and 31520 is 1.

GCF(31509,31520) = 1

We will now calculate the prime factors of 31509 and 31520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31509 and 31520.

How to find the GCF of 31509 and 31520?

We will first find the prime factorization of 31509 and 31520. After we will calculate the factors of 31509 and 31520 and find the biggest common factor number .

Step-1: Prime Factorization of 31509

Prime factors of 31509 are 3, 389. Prime factorization of 31509 in exponential form is:

31509 = 3⁴ × 389¹

Step-2: Prime Factorization of 31520

Prime factors of 31520 are 2, 5, 197. Prime factorization of 31520 in exponential form is:

31520 = 2⁵ × 5¹ × 197¹

Step-3: Factors of 31509

List of positive integer factors of 31509 that divides 31509 without a remainder.

1, 3, 9, 27, 81, 389, 1167, 3501, 10503

Step-4: Factors of 31520

List of positive integer factors of 31520 that divides 31509 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160, 197, 394, 788, 985, 1576, 1970, 3152, 3940, 6304, 7880, 15760

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31509 and 31520. The biggest common factor number is the GCF number.
So the greatest common factor 31509 and 31520 is 1.

Also check out the Least Common Multiple of 31509 and 31520