What is the Greatest Common Factor of 3700 and 3714?

Greatest common factor (GCF) of 3700 and 3714 is 2.

GCF(3700,3714) = 2

We will now calculate the prime factors of 3700 and 3714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3700 and 3714.

How to find the GCF of 3700 and 3714?

We will first find the prime factorization of 3700 and 3714. After we will calculate the factors of 3700 and 3714 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 3714

Prime factors of 3714 are 2, 3, 619. Prime factorization of 3714 in exponential form is:

3714 = 2¹ × 3¹ × 619¹

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 3714

List of positive integer factors of 3714 that divides 3700 without a remainder.

1, 2, 3, 6, 619, 1238, 1857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3700 and 3714. The biggest common factor number is the GCF number.
So the greatest common factor 3700 and 3714 is 2.

Also check out the Least Common Multiple of 3700 and 3714