What is the Greatest Common Factor of 10746 and 10766?

Greatest common factor (GCF) of 10746 and 10766 is 2.

GCF(10746,10766) = 2

We will now calculate the prime factors of 10746 and 10766, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10746 and 10766.

How to find the GCF of 10746 and 10766?

We will first find the prime factorization of 10746 and 10766. After we will calculate the factors of 10746 and 10766 and find the biggest common factor number .

Step-1: Prime Factorization of 10746

Prime factors of 10746 are 2, 3, 199. Prime factorization of 10746 in exponential form is:

10746 = 2¹ × 3³ × 199¹

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 10746

List of positive integer factors of 10746 that divides 10746 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 199, 398, 597, 1194, 1791, 3582, 5373

Step-4: Factors of 10766

List of positive integer factors of 10766 that divides 10746 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10746 and 10766. The biggest common factor number is the GCF number.
So the greatest common factor 10746 and 10766 is 2.

Also check out the Least Common Multiple of 10746 and 10766