What is the Greatest Common Factor of 31734 and 31752?

Greatest common factor (GCF) of 31734 and 31752 is 18.

GCF(31734,31752) = 18

We will now calculate the prime factors of 31734 and 31752, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31734 and 31752.

How to find the GCF of 31734 and 31752?

We will first find the prime factorization of 31734 and 31752. After we will calculate the factors of 31734 and 31752 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31752

Prime factors of 31752 are 2, 3, 7. Prime factorization of 31752 in exponential form is:

31752 = 2³ × 3⁴ × 7²

Step-3: Factors of 31734

List of positive integer factors of 31734 that divides 31734 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

Step-4: Factors of 31752

List of positive integer factors of 31752 that divides 31734 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 49, 54, 56, 63, 72, 81, 84, 98, 108, 126, 147, 162, 168, 189, 196, 216, 252, 294, 324, 378, 392, 441, 504, 567, 588, 648, 756, 882, 1134, 1176, 1323, 1512, 1764, 2268, 2646, 3528, 3969, 4536, 5292, 7938, 10584, 15876

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31734 and 31752. The biggest common factor number is the GCF number.
So the greatest common factor 31734 and 31752 is 18.

Also check out the Least Common Multiple of 31734 and 31752