What is the Greatest Common Factor of 31752 and 31766?

Greatest common factor (GCF) of 31752 and 31766 is 14.

GCF(31752,31766) = 14

We will now calculate the prime factors of 31752 and 31766, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31752 and 31766.

How to find the GCF of 31752 and 31766?

We will first find the prime factorization of 31752 and 31766. After we will calculate the factors of 31752 and 31766 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31766

Prime factors of 31766 are 2, 7, 2269. Prime factorization of 31766 in exponential form is:

31766 = 2¹ × 7¹ × 2269¹

Step-3: Factors of 31752

List of positive integer factors of 31752 that divides 31752 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

Step-4: Factors of 31766

List of positive integer factors of 31766 that divides 31752 without a remainder.

1, 2, 7, 14, 2269, 4538, 15883

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31752 and 31766. The biggest common factor number is the GCF number.
So the greatest common factor 31752 and 31766 is 14.

Also check out the Least Common Multiple of 31752 and 31766