What is the Greatest Common Factor of 10730 and 10734?

Greatest common factor (GCF) of 10730 and 10734 is 2.

GCF(10730,10734) = 2

We will now calculate the prime factors of 10730 and 10734, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10730 and 10734.

How to find the GCF of 10730 and 10734?

We will first find the prime factorization of 10730 and 10734. After we will calculate the factors of 10730 and 10734 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 10734

Prime factors of 10734 are 2, 3, 1789. Prime factorization of 10734 in exponential form is:

10734 = 2¹ × 3¹ × 1789¹

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 10734

List of positive integer factors of 10734 that divides 10730 without a remainder.

1, 2, 3, 6, 1789, 3578, 5367

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10730 and 10734. The biggest common factor number is the GCF number.
So the greatest common factor 10730 and 10734 is 2.

Also check out the Least Common Multiple of 10730 and 10734