What is the Greatest Common Factor of 3700 and 3710?

Greatest common factor (GCF) of 3700 and 3710 is 10.

GCF(3700,3710) = 10

We will now calculate the prime factors of 3700 and 3710, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3700 and 3710.

How to find the GCF of 3700 and 3710?

We will first find the prime factorization of 3700 and 3710. After we will calculate the factors of 3700 and 3710 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 3710

Prime factors of 3710 are 2, 5, 7, 53. Prime factorization of 3710 in exponential form is:

3710 = 2¹ × 5¹ × 7¹ × 53¹

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 3710

List of positive integer factors of 3710 that divides 3700 without a remainder.

1, 2, 5, 7, 10, 14, 35, 53, 70, 106, 265, 371, 530, 742, 1855

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3700 and 3710. The biggest common factor number is the GCF number.
So the greatest common factor 3700 and 3710 is 10.

Also check out the Least Common Multiple of 3700 and 3710