What is the Greatest Common Factor of 3681 and 3696?

Greatest common factor (GCF) of 3681 and 3696 is 3.

GCF(3681,3696) = 3

We will now calculate the prime factors of 3681 and 3696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3681 and 3696.

How to find the GCF of 3681 and 3696?

We will first find the prime factorization of 3681 and 3696. After we will calculate the factors of 3681 and 3696 and find the biggest common factor number .

Step-1: Prime Factorization of 3681

Prime factors of 3681 are 3, 409. Prime factorization of 3681 in exponential form is:

3681 = 3² × 409¹

Step-2: Prime Factorization of 3696

Prime factors of 3696 are 2, 3, 7, 11. Prime factorization of 3696 in exponential form is:

3696 = 2⁴ × 3¹ × 7¹ × 11¹

Step-3: Factors of 3681

List of positive integer factors of 3681 that divides 3681 without a remainder.

1, 3, 9, 409, 1227

Step-4: Factors of 3696

List of positive integer factors of 3696 that divides 3681 without a remainder.

1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 16, 21, 22, 24, 28, 33, 42, 44, 48, 56, 66, 77, 84, 88, 112, 132, 154, 168, 176, 231, 264, 308, 336, 462, 528, 616, 924, 1232, 1848

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3681 and 3696. The biggest common factor number is the GCF number.
So the greatest common factor 3681 and 3696 is 3.

Also check out the Least Common Multiple of 3681 and 3696