What is the Greatest Common Factor of 67800 and 67814?

Greatest common factor (GCF) of 67800 and 67814 is 2.

GCF(67800,67814) = 2

We will now calculate the prime factors of 67800 and 67814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67800 and 67814.

How to find the GCF of 67800 and 67814?

We will first find the prime factorization of 67800 and 67814. After we will calculate the factors of 67800 and 67814 and find the biggest common factor number .

Step-1: Prime Factorization of 67800

Prime factors of 67800 are 2, 3, 5, 113. Prime factorization of 67800 in exponential form is:

67800 = 2³ × 3¹ × 5² × 113¹

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 67800

List of positive integer factors of 67800 that divides 67800 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 113, 120, 150, 200, 226, 300, 339, 452, 565, 600, 678, 904, 1130, 1356, 1695, 2260, 2712, 2825, 3390, 4520, 5650, 6780, 8475, 11300, 13560, 16950, 22600, 33900

Step-4: Factors of 67814

List of positive integer factors of 67814 that divides 67800 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67800 and 67814. The biggest common factor number is the GCF number.
So the greatest common factor 67800 and 67814 is 2.

Also check out the Least Common Multiple of 67800 and 67814