What is the Greatest Common Factor of 31545 and 31560?

Greatest common factor (GCF) of 31545 and 31560 is 15.

GCF(31545,31560) = 15

We will now calculate the prime factors of 31545 and 31560, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31545 and 31560.

How to find the GCF of 31545 and 31560?

We will first find the prime factorization of 31545 and 31560. After we will calculate the factors of 31545 and 31560 and find the biggest common factor number .

Step-1: Prime Factorization of 31545

Prime factors of 31545 are 3, 5, 701. Prime factorization of 31545 in exponential form is:

31545 = 3² × 5¹ × 701¹

Step-2: Prime Factorization of 31560

Prime factors of 31560 are 2, 3, 5, 263. Prime factorization of 31560 in exponential form is:

31560 = 2³ × 3¹ × 5¹ × 263¹

Step-3: Factors of 31545

List of positive integer factors of 31545 that divides 31545 without a remainder.

1, 3, 5, 9, 15, 45, 701, 2103, 3505, 6309, 10515

Step-4: Factors of 31560

List of positive integer factors of 31560 that divides 31545 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 263, 526, 789, 1052, 1315, 1578, 2104, 2630, 3156, 3945, 5260, 6312, 7890, 10520, 15780

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31545 and 31560. The biggest common factor number is the GCF number.
So the greatest common factor 31545 and 31560 is 15.

Also check out the Least Common Multiple of 31545 and 31560