What is the Greatest Common Factor of 11754 and 11774?

Greatest common factor (GCF) of 11754 and 11774 is 2.

GCF(11754,11774) = 2

We will now calculate the prime factors of 11754 and 11774, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11754 and 11774.

How to find the GCF of 11754 and 11774?

We will first find the prime factorization of 11754 and 11774. After we will calculate the factors of 11754 and 11774 and find the biggest common factor number .

Step-1: Prime Factorization of 11754

Prime factors of 11754 are 2, 3, 653. Prime factorization of 11754 in exponential form is:

11754 = 2¹ × 3² × 653¹

Step-2: Prime Factorization of 11774

Prime factors of 11774 are 2, 7, 29. Prime factorization of 11774 in exponential form is:

11774 = 2¹ × 7¹ × 29²

Step-3: Factors of 11754

List of positive integer factors of 11754 that divides 11754 without a remainder.

1, 2, 3, 6, 9, 18, 653, 1306, 1959, 3918, 5877

Step-4: Factors of 11774

List of positive integer factors of 11774 that divides 11754 without a remainder.

1, 2, 7, 14, 29, 58, 203, 406, 841, 1682, 5887

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11754 and 11774. The biggest common factor number is the GCF number.
So the greatest common factor 11754 and 11774 is 2.

Also check out the Least Common Multiple of 11754 and 11774