What is the Greatest Common Factor of 67808 and 67814?

Greatest common factor (GCF) of 67808 and 67814 is 2.

GCF(67808,67814) = 2

We will now calculate the prime factors of 67808 and 67814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67808 and 67814.

How to find the GCF of 67808 and 67814?

We will first find the prime factorization of 67808 and 67814. After we will calculate the factors of 67808 and 67814 and find the biggest common factor number .

Step-1: Prime Factorization of 67808

Prime factors of 67808 are 2, 13, 163. Prime factorization of 67808 in exponential form is:

67808 = 2⁵ × 13¹ × 163¹

Step-2: Prime Factorization of 67814

Prime factors of 67814 are 2, 41, 827. Prime factorization of 67814 in exponential form is:

67814 = 2¹ × 41¹ × 827¹

Step-3: Factors of 67808

List of positive integer factors of 67808 that divides 67808 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 163, 208, 326, 416, 652, 1304, 2119, 2608, 4238, 5216, 8476, 16952, 33904

Step-4: Factors of 67814

List of positive integer factors of 67814 that divides 67808 without a remainder.

1, 2, 41, 82, 827, 1654, 33907

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67808 and 67814. The biggest common factor number is the GCF number.
So the greatest common factor 67808 and 67814 is 2.

Also check out the Least Common Multiple of 67808 and 67814