What is the Greatest Common Factor of 1909 and 1914?

Greatest common factor (GCF) of 1909 and 1914 is 1.

GCF(1909,1914) = 1

We will now calculate the prime factors of 1909 and 1914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1909 and 1914.

How to find the GCF of 1909 and 1914?

We will first find the prime factorization of 1909 and 1914. After we will calculate the factors of 1909 and 1914 and find the biggest common factor number .

Step-1: Prime Factorization of 1909

Prime factors of 1909 are 23, 83. Prime factorization of 1909 in exponential form is:

1909 = 23¹ × 83¹

Step-2: Prime Factorization of 1914

Prime factors of 1914 are 2, 3, 11, 29. Prime factorization of 1914 in exponential form is:

1914 = 2¹ × 3¹ × 11¹ × 29¹

Step-3: Factors of 1909

List of positive integer factors of 1909 that divides 1909 without a remainder.

1, 23, 83

Step-4: Factors of 1914

List of positive integer factors of 1914 that divides 1909 without a remainder.

1, 2, 3, 6, 11, 22, 29, 33, 58, 66, 87, 174, 319, 638, 957

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1909 and 1914. The biggest common factor number is the GCF number.
So the greatest common factor 1909 and 1914 is 1.

Also check out the Least Common Multiple of 1909 and 1914