What is the Greatest Common Factor of 3706 and 3723?

Greatest common factor (GCF) of 3706 and 3723 is 17.

GCF(3706,3723) = 17

We will now calculate the prime factors of 3706 and 3723, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3706 and 3723.

How to find the GCF of 3706 and 3723?

We will first find the prime factorization of 3706 and 3723. After we will calculate the factors of 3706 and 3723 and find the biggest common factor number .

Step-1: Prime Factorization of 3706

Prime factors of 3706 are 2, 17, 109. Prime factorization of 3706 in exponential form is:

3706 = 2¹ × 17¹ × 109¹

Step-2: 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-3: Factors of 3706

List of positive integer factors of 3706 that divides 3706 without a remainder.

1, 2, 17, 34, 109, 218, 1853

Step-4: Factors of 3723

List of positive integer factors of 3723 that divides 3706 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3706 and 3723. The biggest common factor number is the GCF number.
So the greatest common factor 3706 and 3723 is 17.

Also check out the Least Common Multiple of 3706 and 3723