What is the Greatest Common Factor of 11742 and 11754?

Greatest common factor (GCF) of 11742 and 11754 is 6.

GCF(11742,11754) = 6

We will now calculate the prime factors of 11742 and 11754, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11742 and 11754.

How to find the GCF of 11742 and 11754?

We will first find the prime factorization of 11742 and 11754. After we will calculate the factors of 11742 and 11754 and find the biggest common factor number .

Step-1: Prime Factorization of 11742

Prime factors of 11742 are 2, 3, 19, 103. Prime factorization of 11742 in exponential form is:

11742 = 2¹ × 3¹ × 19¹ × 103¹

Step-2: 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-3: Factors of 11742

List of positive integer factors of 11742 that divides 11742 without a remainder.

1, 2, 3, 6, 19, 38, 57, 103, 114, 206, 309, 618, 1957, 3914, 5871

Step-4: Factors of 11754

List of positive integer factors of 11754 that divides 11742 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11742 and 11754. The biggest common factor number is the GCF number.
So the greatest common factor 11742 and 11754 is 6.

Also check out the Least Common Multiple of 11742 and 11754