What is the Greatest Common Factor of 17814 and 17824?

Greatest common factor (GCF) of 17814 and 17824 is 2.

GCF(17814,17824) = 2

We will now calculate the prime factors of 17814 and 17824, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17814 and 17824.

How to find the GCF of 17814 and 17824?

We will first find the prime factorization of 17814 and 17824. After we will calculate the factors of 17814 and 17824 and find the biggest common factor number .

Step-1: Prime Factorization of 17814

Prime factors of 17814 are 2, 3, 2969. Prime factorization of 17814 in exponential form is:

17814 = 2¹ × 3¹ × 2969¹

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 17814

List of positive integer factors of 17814 that divides 17814 without a remainder.

1, 2, 3, 6, 2969, 5938, 8907

Step-4: Factors of 17824

List of positive integer factors of 17824 that divides 17814 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 17814 and 17824. The biggest common factor number is the GCF number.
So the greatest common factor 17814 and 17824 is 2.

Also check out the Least Common Multiple of 17814 and 17824