What is the Greatest Common Factor of 10766 and 10774?

Greatest common factor (GCF) of 10766 and 10774 is 2.

GCF(10766,10774) = 2

We will now calculate the prime factors of 10766 and 10774, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10766 and 10774.

How to find the GCF of 10766 and 10774?

We will first find the prime factorization of 10766 and 10774. After we will calculate the factors of 10766 and 10774 and find the biggest common factor number .

Step-1: Prime Factorization of 10766

Prime factors of 10766 are 2, 7, 769. Prime factorization of 10766 in exponential form is:

10766 = 2¹ × 7¹ × 769¹

Step-2: Prime Factorization of 10774

Prime factors of 10774 are 2, 5387. Prime factorization of 10774 in exponential form is:

10774 = 2¹ × 5387¹

Step-3: Factors of 10766

List of positive integer factors of 10766 that divides 10766 without a remainder.

1, 2, 7, 14, 769, 1538, 5383

Step-4: Factors of 10774

List of positive integer factors of 10774 that divides 10766 without a remainder.

1, 2, 5387

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10766 and 10774. The biggest common factor number is the GCF number.
So the greatest common factor 10766 and 10774 is 2.

Also check out the Least Common Multiple of 10766 and 10774