What is the Greatest Common Factor of 3744 and 3762?

Greatest common factor (GCF) of 3744 and 3762 is 18.

GCF(3744,3762) = 18

We will now calculate the prime factors of 3744 and 3762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3744 and 3762.

How to find the GCF of 3744 and 3762?

We will first find the prime factorization of 3744 and 3762. After we will calculate the factors of 3744 and 3762 and find the biggest common factor number .

Step-1: Prime Factorization of 3744

Prime factors of 3744 are 2, 3, 13. Prime factorization of 3744 in exponential form is:

3744 = 2⁵ × 3² × 13¹

Step-2: Prime Factorization of 3762

Prime factors of 3762 are 2, 3, 11, 19. Prime factorization of 3762 in exponential form is:

3762 = 2¹ × 3² × 11¹ × 19¹

Step-3: Factors of 3744

List of positive integer factors of 3744 that divides 3744 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 32, 36, 39, 48, 52, 72, 78, 96, 104, 117, 144, 156, 208, 234, 288, 312, 416, 468, 624, 936, 1248, 1872

Step-4: Factors of 3762

List of positive integer factors of 3762 that divides 3744 without a remainder.

1, 2, 3, 6, 9, 11, 18, 19, 22, 33, 38, 57, 66, 99, 114, 171, 198, 209, 342, 418, 627, 1254, 1881

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3744 and 3762. The biggest common factor number is the GCF number.
So the greatest common factor 3744 and 3762 is 18.

Also check out the Least Common Multiple of 3744 and 3762