What is the Greatest Common Factor of 17806 and 17824?

Greatest common factor (GCF) of 17806 and 17824 is 2.

GCF(17806,17824) = 2

We will now calculate the prime factors of 17806 and 17824, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17806 and 17824.

How to find the GCF of 17806 and 17824?

We will first find the prime factorization of 17806 and 17824. After we will calculate the factors of 17806 and 17824 and find the biggest common factor number .

Step-1: Prime Factorization of 17806

Prime factors of 17806 are 2, 29, 307. Prime factorization of 17806 in exponential form is:

17806 = 2¹ × 29¹ × 307¹

Step-2: Prime Factorization of 17824

Prime factors of 17824 are 2, 557. Prime factorization of 17824 in exponential form is:

17824 = 2⁵ × 557¹

Step-3: Factors of 17806

List of positive integer factors of 17806 that divides 17806 without a remainder.

1, 2, 29, 58, 307, 614, 8903

Step-4: Factors of 17824

List of positive integer factors of 17824 that divides 17806 without a remainder.

1, 2, 4, 8, 16, 32, 557, 1114, 2228, 4456, 8912

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17806 and 17824. The biggest common factor number is the GCF number.
So the greatest common factor 17806 and 17824 is 2.

Also check out the Least Common Multiple of 17806 and 17824