What is the Greatest Common Factor of 9800 and 9814?

Greatest common factor (GCF) of 9800 and 9814 is 14.

GCF(9800,9814) = 14

We will now calculate the prime factors of 9800 and 9814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9800 and 9814.

How to find the GCF of 9800 and 9814?

We will first find the prime factorization of 9800 and 9814. After we will calculate the factors of 9800 and 9814 and find the biggest common factor number .

Step-1: Prime Factorization of 9800

Prime factors of 9800 are 2, 5, 7. Prime factorization of 9800 in exponential form is:

9800 = 2³ × 5² × 7²

Step-2: Prime Factorization of 9814

Prime factors of 9814 are 2, 7, 701. Prime factorization of 9814 in exponential form is:

9814 = 2¹ × 7¹ × 701¹

Step-3: Factors of 9800

List of positive integer factors of 9800 that divides 9800 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 49, 50, 56, 70, 98, 100, 140, 175, 196, 200, 245, 280, 350, 392, 490, 700, 980, 1225, 1400, 1960, 2450, 4900

Step-4: Factors of 9814

List of positive integer factors of 9814 that divides 9800 without a remainder.

1, 2, 7, 14, 701, 1402, 4907

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9800 and 9814. The biggest common factor number is the GCF number.
So the greatest common factor 9800 and 9814 is 14.

Also check out the Least Common Multiple of 9800 and 9814