What is the Greatest Common Factor of 69800 and 69814?

Greatest common factor (GCF) of 69800 and 69814 is 2.

GCF(69800,69814) = 2

We will now calculate the prime factors of 69800 and 69814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69800 and 69814.

How to find the GCF of 69800 and 69814?

We will first find the prime factorization of 69800 and 69814. After we will calculate the factors of 69800 and 69814 and find the biggest common factor number .

Step-1: Prime Factorization of 69800

Prime factors of 69800 are 2, 5, 349. Prime factorization of 69800 in exponential form is:

69800 = 2³ × 5² × 349¹

Step-2: Prime Factorization of 69814

Prime factors of 69814 are 2, 67, 521. Prime factorization of 69814 in exponential form is:

69814 = 2¹ × 67¹ × 521¹

Step-3: Factors of 69800

List of positive integer factors of 69800 that divides 69800 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200, 349, 698, 1396, 1745, 2792, 3490, 6980, 8725, 13960, 17450, 34900

Step-4: Factors of 69814

List of positive integer factors of 69814 that divides 69800 without a remainder.

1, 2, 67, 134, 521, 1042, 34907

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69800 and 69814. The biggest common factor number is the GCF number.
So the greatest common factor 69800 and 69814 is 2.

Also check out the Least Common Multiple of 69800 and 69814