What is the Greatest Common Factor of 3692 and 3705?

Greatest common factor (GCF) of 3692 and 3705 is 13.

GCF(3692,3705) = 13

We will now calculate the prime factors of 3692 and 3705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3692 and 3705.

How to find the GCF of 3692 and 3705?

We will first find the prime factorization of 3692 and 3705. After we will calculate the factors of 3692 and 3705 and find the biggest common factor number .

Step-1: Prime Factorization of 3692

Prime factors of 3692 are 2, 13, 71. Prime factorization of 3692 in exponential form is:

3692 = 2² × 13¹ × 71¹

Step-2: Prime Factorization of 3705

Prime factors of 3705 are 3, 5, 13, 19. Prime factorization of 3705 in exponential form is:

3705 = 3¹ × 5¹ × 13¹ × 19¹

Step-3: Factors of 3692

List of positive integer factors of 3692 that divides 3692 without a remainder.

1, 2, 4, 13, 26, 52, 71, 142, 284, 923, 1846

Step-4: Factors of 3705

List of positive integer factors of 3705 that divides 3692 without a remainder.

1, 3, 5, 13, 15, 19, 39, 57, 65, 95, 195, 247, 285, 741, 1235

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3692 and 3705. The biggest common factor number is the GCF number.
So the greatest common factor 3692 and 3705 is 13.

Also check out the Least Common Multiple of 3692 and 3705