What is the Greatest Common Factor of 3744 and 3750?

Greatest common factor (GCF) of 3744 and 3750 is 6.

GCF(3744,3750) = 6

We will now calculate the prime factors of 3744 and 3750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3744 and 3750.

How to find the GCF of 3744 and 3750?

We will first find the prime factorization of 3744 and 3750. After we will calculate the factors of 3744 and 3750 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 3750

Prime factors of 3750 are 2, 3, 5. Prime factorization of 3750 in exponential form is:

3750 = 2¹ × 3¹ × 5⁴

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 3750

List of positive integer factors of 3750 that divides 3744 without a remainder.

1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 625, 750, 1250, 1875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3744 and 3750. The biggest common factor number is the GCF number.
So the greatest common factor 3744 and 3750 is 6.

Also check out the Least Common Multiple of 3744 and 3750