What is the Greatest Common Factor of 1909 and 1917?

Greatest common factor (GCF) of 1909 and 1917 is 1.

GCF(1909,1917) = 1

We will now calculate the prime factors of 1909 and 1917, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1909 and 1917.

How to find the GCF of 1909 and 1917?

We will first find the prime factorization of 1909 and 1917. After we will calculate the factors of 1909 and 1917 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 1917

Prime factors of 1917 are 3, 71. Prime factorization of 1917 in exponential form is:

1917 = 3³ × 71¹

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 1917

List of positive integer factors of 1917 that divides 1909 without a remainder.

1, 3, 9, 27, 71, 213, 639

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1909 and 1917. The biggest common factor number is the GCF number.
So the greatest common factor 1909 and 1917 is 1.

Also check out the Least Common Multiple of 1909 and 1917