What is the Greatest Common Factor of 10731 and 10749?

Greatest common factor (GCF) of 10731 and 10749 is 3.

GCF(10731,10749) = 3

We will now calculate the prime factors of 10731 and 10749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10731 and 10749.

How to find the GCF of 10731 and 10749?

We will first find the prime factorization of 10731 and 10749. After we will calculate the factors of 10731 and 10749 and find the biggest common factor number .

Step-1: Prime Factorization of 10731

Prime factors of 10731 are 3, 7, 73. Prime factorization of 10731 in exponential form is:

10731 = 3¹ × 7² × 73¹

Step-2: Prime Factorization of 10749

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

10749 = 3¹ × 3583¹

Step-3: Factors of 10731

List of positive integer factors of 10731 that divides 10731 without a remainder.

1, 3, 7, 21, 49, 73, 147, 219, 511, 1533, 3577

Step-4: Factors of 10749

List of positive integer factors of 10749 that divides 10731 without a remainder.

1, 3, 3583

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10731 and 10749. The biggest common factor number is the GCF number.
So the greatest common factor 10731 and 10749 is 3.

Also check out the Least Common Multiple of 10731 and 10749