What is the Greatest Common Factor of 17728 and 17746?

Greatest common factor (GCF) of 17728 and 17746 is 2.

GCF(17728,17746) = 2

We will now calculate the prime factors of 17728 and 17746, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17728 and 17746.

How to find the GCF of 17728 and 17746?

We will first find the prime factorization of 17728 and 17746. After we will calculate the factors of 17728 and 17746 and find the biggest common factor number .

Step-1: Prime Factorization of 17728

Prime factors of 17728 are 2, 277. Prime factorization of 17728 in exponential form is:

17728 = 2⁶ × 277¹

Step-2: Prime Factorization of 17746

Prime factors of 17746 are 2, 19, 467. Prime factorization of 17746 in exponential form is:

17746 = 2¹ × 19¹ × 467¹

Step-3: Factors of 17728

List of positive integer factors of 17728 that divides 17728 without a remainder.

1, 2, 4, 8, 16, 32, 64, 277, 554, 1108, 2216, 4432, 8864

Step-4: Factors of 17746

List of positive integer factors of 17746 that divides 17728 without a remainder.

1, 2, 19, 38, 467, 934, 8873

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17728 and 17746. The biggest common factor number is the GCF number.
So the greatest common factor 17728 and 17746 is 2.

Also check out the Least Common Multiple of 17728 and 17746