What is the Greatest Common Factor of 3774 and 3780?

Greatest common factor (GCF) of 3774 and 3780 is 6.

GCF(3774,3780) = 6

We will now calculate the prime factors of 3774 and 3780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3774 and 3780.

How to find the GCF of 3774 and 3780?

We will first find the prime factorization of 3774 and 3780. After we will calculate the factors of 3774 and 3780 and find the biggest common factor number .

Step-1: Prime Factorization of 3774

Prime factors of 3774 are 2, 3, 17, 37. Prime factorization of 3774 in exponential form is:

3774 = 2¹ × 3¹ × 17¹ × 37¹

Step-2: Prime Factorization of 3780

Prime factors of 3780 are 2, 3, 5, 7. Prime factorization of 3780 in exponential form is:

3780 = 2² × 3³ × 5¹ × 7¹

Step-3: Factors of 3774

List of positive integer factors of 3774 that divides 3774 without a remainder.

1, 2, 3, 6, 17, 34, 37, 51, 74, 102, 111, 222, 629, 1258, 1887

Step-4: Factors of 3780

List of positive integer factors of 3780 that divides 3774 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 27, 28, 30, 35, 36, 42, 45, 54, 60, 63, 70, 84, 90, 105, 108, 126, 135, 140, 180, 189, 210, 252, 270, 315, 378, 420, 540, 630, 756, 945, 1260, 1890

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3774 and 3780. The biggest common factor number is the GCF number.
So the greatest common factor 3774 and 3780 is 6.

Also check out the Least Common Multiple of 3774 and 3780