What is the Greatest Common Factor of 31632 and 31647?

Greatest common factor (GCF) of 31632 and 31647 is 3.

GCF(31632,31647) = 3

We will now calculate the prime factors of 31632 and 31647, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31632 and 31647.

How to find the GCF of 31632 and 31647?

We will first find the prime factorization of 31632 and 31647. After we will calculate the factors of 31632 and 31647 and find the biggest common factor number .

Step-1: Prime Factorization of 31632

Prime factors of 31632 are 2, 3, 659. Prime factorization of 31632 in exponential form is:

31632 = 2⁴ × 3¹ × 659¹

Step-2: Prime Factorization of 31647

Prime factors of 31647 are 3, 7, 11, 137. Prime factorization of 31647 in exponential form is:

31647 = 3¹ × 7¹ × 11¹ × 137¹

Step-3: Factors of 31632

List of positive integer factors of 31632 that divides 31632 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 659, 1318, 1977, 2636, 3954, 5272, 7908, 10544, 15816

Step-4: Factors of 31647

List of positive integer factors of 31647 that divides 31632 without a remainder.

1, 3, 7, 11, 21, 33, 77, 137, 231, 411, 959, 1507, 2877, 4521, 10549

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31632 and 31647. The biggest common factor number is the GCF number.
So the greatest common factor 31632 and 31647 is 3.

Also check out the Least Common Multiple of 31632 and 31647