What is the Greatest Common Factor of 17804 and 17814?

Greatest common factor (GCF) of 17804 and 17814 is 2.

GCF(17804,17814) = 2

We will now calculate the prime factors of 17804 and 17814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17804 and 17814.

How to find the GCF of 17804 and 17814?

We will first find the prime factorization of 17804 and 17814. After we will calculate the factors of 17804 and 17814 and find the biggest common factor number .

Step-1: Prime Factorization of 17804

Prime factors of 17804 are 2, 4451. Prime factorization of 17804 in exponential form is:

17804 = 2² × 4451¹

Step-2: 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-3: Factors of 17804

List of positive integer factors of 17804 that divides 17804 without a remainder.

1, 2, 4, 4451, 8902

Step-4: Factors of 17814

List of positive integer factors of 17814 that divides 17804 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17804 and 17814. The biggest common factor number is the GCF number.
So the greatest common factor 17804 and 17814 is 2.

Also check out the Least Common Multiple of 17804 and 17814