What is the Greatest Common Factor of 10766 and 10780?

Greatest common factor (GCF) of 10766 and 10780 is 14.

GCF(10766,10780) = 14

We will now calculate the prime factors of 10766 and 10780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10766 and 10780.

How to find the GCF of 10766 and 10780?

We will first find the prime factorization of 10766 and 10780. After we will calculate the factors of 10766 and 10780 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 10780

Prime factors of 10780 are 2, 5, 7, 11. Prime factorization of 10780 in exponential form is:

10780 = 2² × 5¹ × 7² × 11¹

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 10780

List of positive integer factors of 10780 that divides 10766 without a remainder.

1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 28, 35, 44, 49, 55, 70, 77, 98, 110, 140, 154, 196, 220, 245, 308, 385, 490, 539, 770, 980, 1078, 1540, 2156, 2695, 5390

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10766 and 10780. The biggest common factor number is the GCF number.
So the greatest common factor 10766 and 10780 is 14.

Also check out the Least Common Multiple of 10766 and 10780