What is the Greatest Common Factor of 10749 and 10761?

Greatest common factor (GCF) of 10749 and 10761 is 3.

GCF(10749,10761) = 3

We will now calculate the prime factors of 10749 and 10761, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10749 and 10761.

How to find the GCF of 10749 and 10761?

We will first find the prime factorization of 10749 and 10761. After we will calculate the factors of 10749 and 10761 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 10761

Prime factors of 10761 are 3, 17, 211. Prime factorization of 10761 in exponential form is:

10761 = 3¹ × 17¹ × 211¹

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 10761

List of positive integer factors of 10761 that divides 10749 without a remainder.

1, 3, 17, 51, 211, 633, 3587

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10749 and 10761. The biggest common factor number is the GCF number.
So the greatest common factor 10749 and 10761 is 3.

Also check out the Least Common Multiple of 10749 and 10761