What is the Greatest Common Factor of 3724 and 3738?

Greatest common factor (GCF) of 3724 and 3738 is 14.

GCF(3724,3738) = 14

We will now calculate the prime factors of 3724 and 3738, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3724 and 3738.

How to find the GCF of 3724 and 3738?

We will first find the prime factorization of 3724 and 3738. After we will calculate the factors of 3724 and 3738 and find the biggest common factor number .

Step-1: Prime Factorization of 3724

Prime factors of 3724 are 2, 7, 19. Prime factorization of 3724 in exponential form is:

3724 = 2² × 7² × 19¹

Step-2: Prime Factorization of 3738

Prime factors of 3738 are 2, 3, 7, 89. Prime factorization of 3738 in exponential form is:

3738 = 2¹ × 3¹ × 7¹ × 89¹

Step-3: Factors of 3724

List of positive integer factors of 3724 that divides 3724 without a remainder.

1, 2, 4, 7, 14, 19, 28, 38, 49, 76, 98, 133, 196, 266, 532, 931, 1862

Step-4: Factors of 3738

List of positive integer factors of 3738 that divides 3724 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 89, 178, 267, 534, 623, 1246, 1869

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3724 and 3738. The biggest common factor number is the GCF number.
So the greatest common factor 3724 and 3738 is 14.

Also check out the Least Common Multiple of 3724 and 3738