What is the Greatest Common Factor of 3723 and 3740?

Greatest common factor (GCF) of 3723 and 3740 is 17.

GCF(3723,3740) = 17

We will now calculate the prime factors of 3723 and 3740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3723 and 3740.

How to find the GCF of 3723 and 3740?

We will first find the prime factorization of 3723 and 3740. After we will calculate the factors of 3723 and 3740 and find the biggest common factor number .

Step-1: Prime Factorization of 3723

Prime factors of 3723 are 3, 17, 73. Prime factorization of 3723 in exponential form is:

3723 = 3¹ × 17¹ × 73¹

Step-2: Prime Factorization of 3740

Prime factors of 3740 are 2, 5, 11, 17. Prime factorization of 3740 in exponential form is:

3740 = 2² × 5¹ × 11¹ × 17¹

Step-3: Factors of 3723

List of positive integer factors of 3723 that divides 3723 without a remainder.

1, 3, 17, 51, 73, 219, 1241

Step-4: Factors of 3740

List of positive integer factors of 3740 that divides 3723 without a remainder.

1, 2, 4, 5, 10, 11, 17, 20, 22, 34, 44, 55, 68, 85, 110, 170, 187, 220, 340, 374, 748, 935, 1870

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3723 and 3740. The biggest common factor number is the GCF number.
So the greatest common factor 3723 and 3740 is 17.

Also check out the Least Common Multiple of 3723 and 3740