What is the Greatest Common Factor of 31743 and 31752?

Greatest common factor (GCF) of 31743 and 31752 is 9.

GCF(31743,31752) = 9

We will now calculate the prime factors of 31743 and 31752, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31743 and 31752.

How to find the GCF of 31743 and 31752?

We will first find the prime factorization of 31743 and 31752. After we will calculate the factors of 31743 and 31752 and find the biggest common factor number .

Step-1: Prime Factorization of 31743

Prime factors of 31743 are 3, 3527. Prime factorization of 31743 in exponential form is:

31743 = 3² × 3527¹

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 31743

List of positive integer factors of 31743 that divides 31743 without a remainder.

1, 3, 9, 3527, 10581

Step-4: Factors of 31752

List of positive integer factors of 31752 that divides 31743 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 31743 and 31752. The biggest common factor number is the GCF number.
So the greatest common factor 31743 and 31752 is 9.

Also check out the Least Common Multiple of 31743 and 31752