What is the Greatest Common Factor of 18900 and 18914?

Greatest common factor (GCF) of 18900 and 18914 is 14.

GCF(18900,18914) = 14

We will now calculate the prime factors of 18900 and 18914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 18900 and 18914.

How to find the GCF of 18900 and 18914?

We will first find the prime factorization of 18900 and 18914. After we will calculate the factors of 18900 and 18914 and find the biggest common factor number .

Step-1: Prime Factorization of 18900

Prime factors of 18900 are 2, 3, 5, 7. Prime factorization of 18900 in exponential form is:

18900 = 2² × 3³ × 5² × 7¹

Step-2: Prime Factorization of 18914

Prime factors of 18914 are 2, 7, 193. Prime factorization of 18914 in exponential form is:

18914 = 2¹ × 7² × 193¹

Step-3: Factors of 18900

List of positive integer factors of 18900 that divides 18900 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 25, 27, 28, 30, 35, 36, 42, 45, 50, 54, 60, 63, 70, 75, 84, 90, 100, 105, 108, 126, 135, 140, 150, 175, 180, 189, 210, 225, 252, 270, 300, 315, 350, 378, 420, 450, 525, 540, 630, 675, 700, 756, 900, 945, 1050, 1260, 1350, 1575, 1890, 2100, 2700, 3150, 3780, 4725, 6300, 9450

Step-4: Factors of 18914

List of positive integer factors of 18914 that divides 18900 without a remainder.

1, 2, 7, 14, 49, 98, 193, 386, 1351, 2702, 9457

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 18900 and 18914. The biggest common factor number is the GCF number.
So the greatest common factor 18900 and 18914 is 14.

Also check out the Least Common Multiple of 18900 and 18914