What is the Greatest Common Factor of 31752 and 31765?

Greatest common factor (GCF) of 31752 and 31765 is 1.

GCF(31752,31765) = 1

We will now calculate the prime factors of 31752 and 31765, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31752 and 31765.

How to find the GCF of 31752 and 31765?

We will first find the prime factorization of 31752 and 31765. After we will calculate the factors of 31752 and 31765 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 31765

Prime factors of 31765 are 5, 6353. Prime factorization of 31765 in exponential form is:

31765 = 5¹ × 6353¹

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 31765

List of positive integer factors of 31765 that divides 31752 without a remainder.

1, 5, 6353

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31752 and 31765. The biggest common factor number is the GCF number.
So the greatest common factor 31752 and 31765 is 1.

Also check out the Least Common Multiple of 31752 and 31765