What is the Greatest Common Factor of 3688 and 3696?

Greatest common factor (GCF) of 3688 and 3696 is 8.

GCF(3688,3696) = 8

We will now calculate the prime factors of 3688 and 3696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3688 and 3696.

How to find the GCF of 3688 and 3696?

We will first find the prime factorization of 3688 and 3696. After we will calculate the factors of 3688 and 3696 and find the biggest common factor number .

Step-1: Prime Factorization of 3688

Prime factors of 3688 are 2, 461. Prime factorization of 3688 in exponential form is:

3688 = 2³ × 461¹

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 3688

List of positive integer factors of 3688 that divides 3688 without a remainder.

1, 2, 4, 8, 461, 922, 1844

Step-4: Factors of 3696

List of positive integer factors of 3696 that divides 3688 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 3688 and 3696. The biggest common factor number is the GCF number.
So the greatest common factor 3688 and 3696 is 8.

Also check out the Least Common Multiple of 3688 and 3696