What is the Greatest Common Factor of 3670 and 3680?

Greatest common factor (GCF) of 3670 and 3680 is 10.

GCF(3670,3680) = 10

We will now calculate the prime factors of 3670 and 3680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3670 and 3680.

How to find the GCF of 3670 and 3680?

We will first find the prime factorization of 3670 and 3680. After we will calculate the factors of 3670 and 3680 and find the biggest common factor number .

Step-1: Prime Factorization of 3670

Prime factors of 3670 are 2, 5, 367. Prime factorization of 3670 in exponential form is:

3670 = 2¹ × 5¹ × 367¹

Step-2: Prime Factorization of 3680

Prime factors of 3680 are 2, 5, 23. Prime factorization of 3680 in exponential form is:

3680 = 2⁵ × 5¹ × 23¹

Step-3: Factors of 3670

List of positive integer factors of 3670 that divides 3670 without a remainder.

1, 2, 5, 10, 367, 734, 1835

Step-4: Factors of 3680

List of positive integer factors of 3680 that divides 3670 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 23, 32, 40, 46, 80, 92, 115, 160, 184, 230, 368, 460, 736, 920, 1840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3670 and 3680. The biggest common factor number is the GCF number.
So the greatest common factor 3670 and 3680 is 10.

Also check out the Least Common Multiple of 3670 and 3680