What is the Greatest Common Factor of 10730 and 10746?

Greatest common factor (GCF) of 10730 and 10746 is 2.

GCF(10730,10746) = 2

We will now calculate the prime factors of 10730 and 10746, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10730 and 10746.

How to find the GCF of 10730 and 10746?

We will first find the prime factorization of 10730 and 10746. After we will calculate the factors of 10730 and 10746 and find the biggest common factor number .

Step-1: Prime Factorization of 10730

Prime factors of 10730 are 2, 5, 29, 37. Prime factorization of 10730 in exponential form is:

10730 = 2¹ × 5¹ × 29¹ × 37¹

Step-2: 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-3: Factors of 10730

List of positive integer factors of 10730 that divides 10730 without a remainder.

1, 2, 5, 10, 29, 37, 58, 74, 145, 185, 290, 370, 1073, 2146, 5365

Step-4: Factors of 10746

List of positive integer factors of 10746 that divides 10730 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10730 and 10746. The biggest common factor number is the GCF number.
So the greatest common factor 10730 and 10746 is 2.

Also check out the Least Common Multiple of 10730 and 10746