What is the Greatest Common Factor of 10749 and 10760?

Greatest common factor (GCF) of 10749 and 10760 is 1.

GCF(10749,10760) = 1

We will now calculate the prime factors of 10749 and 10760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10749 and 10760.

How to find the GCF of 10749 and 10760?

We will first find the prime factorization of 10749 and 10760. After we will calculate the factors of 10749 and 10760 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 10760

Prime factors of 10760 are 2, 5, 269. Prime factorization of 10760 in exponential form is:

10760 = 2³ × 5¹ × 269¹

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 10760

List of positive integer factors of 10760 that divides 10749 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40, 269, 538, 1076, 1345, 2152, 2690, 5380

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10749 and 10760. The biggest common factor number is the GCF number.
So the greatest common factor 10749 and 10760 is 1.

Also check out the Least Common Multiple of 10749 and 10760