What is the Greatest Common Factor of 16807 and 16814?

Greatest common factor (GCF) of 16807 and 16814 is 7.

GCF(16807,16814) = 7

We will now calculate the prime factors of 16807 and 16814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16807 and 16814.

How to find the GCF of 16807 and 16814?

We will first find the prime factorization of 16807 and 16814. After we will calculate the factors of 16807 and 16814 and find the biggest common factor number .

Step-1: Prime Factorization of 16807

Prime factors of 16807 are 7. Prime factorization of 16807 in exponential form is:

16807 = 7⁵

Step-2: Prime Factorization of 16814

Prime factors of 16814 are 2, 7, 1201. Prime factorization of 16814 in exponential form is:

16814 = 2¹ × 7¹ × 1201¹

Step-3: Factors of 16807

List of positive integer factors of 16807 that divides 16807 without a remainder.

1, 7, 49, 343, 2401

Step-4: Factors of 16814

List of positive integer factors of 16814 that divides 16807 without a remainder.

1, 2, 7, 14, 1201, 2402, 8407

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16807 and 16814. The biggest common factor number is the GCF number.
So the greatest common factor 16807 and 16814 is 7.

Also check out the Least Common Multiple of 16807 and 16814