What is the Greatest Common Factor of 3700 and 3712?

Greatest common factor (GCF) of 3700 and 3712 is 4.

GCF(3700,3712) = 4

We will now calculate the prime factors of 3700 and 3712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3700 and 3712.

How to find the GCF of 3700 and 3712?

We will first find the prime factorization of 3700 and 3712. After we will calculate the factors of 3700 and 3712 and find the biggest common factor number .

Step-1: Prime Factorization of 3700

Prime factors of 3700 are 2, 5, 37. Prime factorization of 3700 in exponential form is:

3700 = 2² × 5² × 37¹

Step-2: Prime Factorization of 3712

Prime factors of 3712 are 2, 29. Prime factorization of 3712 in exponential form is:

3712 = 2⁷ × 29¹

Step-3: Factors of 3700

List of positive integer factors of 3700 that divides 3700 without a remainder.

1, 2, 4, 5, 10, 20, 25, 37, 50, 74, 100, 148, 185, 370, 740, 925, 1850

Step-4: Factors of 3712

List of positive integer factors of 3712 that divides 3700 without a remainder.

1, 2, 4, 8, 16, 29, 32, 58, 64, 116, 128, 232, 464, 928, 1856

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3700 and 3712. The biggest common factor number is the GCF number.
So the greatest common factor 3700 and 3712 is 4.

Also check out the Least Common Multiple of 3700 and 3712