What is the Greatest Common Factor of 31725 and 31734?

Greatest common factor (GCF) of 31725 and 31734 is 9.

GCF(31725,31734) = 9

We will now calculate the prime factors of 31725 and 31734, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31725 and 31734.

How to find the GCF of 31725 and 31734?

We will first find the prime factorization of 31725 and 31734. After we will calculate the factors of 31725 and 31734 and find the biggest common factor number .

Step-1: Prime Factorization of 31725

Prime factors of 31725 are 3, 5, 47. Prime factorization of 31725 in exponential form is:

31725 = 3³ × 5² × 47¹

Step-2: Prime Factorization of 31734

Prime factors of 31734 are 2, 3, 41, 43. Prime factorization of 31734 in exponential form is:

31734 = 2¹ × 3² × 41¹ × 43¹

Step-3: Factors of 31725

List of positive integer factors of 31725 that divides 31725 without a remainder.

1, 3, 5, 9, 15, 25, 27, 45, 47, 75, 135, 141, 225, 235, 423, 675, 705, 1175, 1269, 2115, 3525, 6345, 10575

Step-4: Factors of 31734

List of positive integer factors of 31734 that divides 31725 without a remainder.

1, 2, 3, 6, 9, 18, 41, 43, 82, 86, 123, 129, 246, 258, 369, 387, 738, 774, 1763, 3526, 5289, 10578, 15867

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31725 and 31734. The biggest common factor number is the GCF number.
So the greatest common factor 31725 and 31734 is 9.

Also check out the Least Common Multiple of 31725 and 31734