What is the Greatest Common Factor of 10730 and 10748?

Greatest common factor (GCF) of 10730 and 10748 is 2.

GCF(10730,10748) = 2

We will now calculate the prime factors of 10730 and 10748, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10730 and 10748.

How to find the GCF of 10730 and 10748?

We will first find the prime factorization of 10730 and 10748. After we will calculate the factors of 10730 and 10748 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 10748

Prime factors of 10748 are 2, 2687. Prime factorization of 10748 in exponential form is:

10748 = 2² × 2687¹

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 10748

List of positive integer factors of 10748 that divides 10730 without a remainder.

1, 2, 4, 2687, 5374

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10730 and 10748. The biggest common factor number is the GCF number.
So the greatest common factor 10730 and 10748 is 2.

Also check out the Least Common Multiple of 10730 and 10748