What is the Greatest Common Factor of 3743 and 3762?

Greatest common factor (GCF) of 3743 and 3762 is 19.

GCF(3743,3762) = 19

We will now calculate the prime factors of 3743 and 3762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3743 and 3762.

How to find the GCF of 3743 and 3762?

We will first find the prime factorization of 3743 and 3762. After we will calculate the factors of 3743 and 3762 and find the biggest common factor number .

Step-1: Prime Factorization of 3743

Prime factors of 3743 are 19, 197. Prime factorization of 3743 in exponential form is:

3743 = 19¹ × 197¹

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 3743

List of positive integer factors of 3743 that divides 3743 without a remainder.

1, 19, 197

Step-4: Factors of 3762

List of positive integer factors of 3762 that divides 3743 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 3743 and 3762. The biggest common factor number is the GCF number.
So the greatest common factor 3743 and 3762 is 19.

Also check out the Least Common Multiple of 3743 and 3762