What is the Greatest Common Factor of 3705 and 3720?

Greatest common factor (GCF) of 3705 and 3720 is 15.

GCF(3705,3720) = 15

We will now calculate the prime factors of 3705 and 3720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3705 and 3720.

How to find the GCF of 3705 and 3720?

We will first find the prime factorization of 3705 and 3720. After we will calculate the factors of 3705 and 3720 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 3720

Prime factors of 3720 are 2, 3, 5, 31. Prime factorization of 3720 in exponential form is:

3720 = 2³ × 3¹ × 5¹ × 31¹

Step-3: Factors of 3705

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

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

Step-4: Factors of 3720

List of positive integer factors of 3720 that divides 3705 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 31, 40, 60, 62, 93, 120, 124, 155, 186, 248, 310, 372, 465, 620, 744, 930, 1240, 1860

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3705 and 3720. The biggest common factor number is the GCF number.
So the greatest common factor 3705 and 3720 is 15.

Also check out the Least Common Multiple of 3705 and 3720