What is the Greatest Common Factor of 10749 and 10766?

Greatest common factor (GCF) of 10749 and 10766 is 1.

GCF(10749,10766) = 1

We will now calculate the prime factors of 10749 and 10766, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10749 and 10766.

How to find the GCF of 10749 and 10766?

We will first find the prime factorization of 10749 and 10766. After we will calculate the factors of 10749 and 10766 and find the biggest common factor number .

Step-1: Prime Factorization of 10749

Prime factors of 10749 are 3, 3583. Prime factorization of 10749 in exponential form is:

10749 = 3¹ × 3583¹

Step-2: 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-3: Factors of 10749

List of positive integer factors of 10749 that divides 10749 without a remainder.

1, 3, 3583

Step-4: Factors of 10766

List of positive integer factors of 10766 that divides 10749 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10749 and 10766. The biggest common factor number is the GCF number.
So the greatest common factor 10749 and 10766 is 1.

Also check out the Least Common Multiple of 10749 and 10766