What is the Greatest Common Factor of 1891 and 1909?

Greatest common factor (GCF) of 1891 and 1909 is 1.

GCF(1891,1909) = 1

We will now calculate the prime factors of 1891 and 1909, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1891 and 1909.

How to find the GCF of 1891 and 1909?

We will first find the prime factorization of 1891 and 1909. After we will calculate the factors of 1891 and 1909 and find the biggest common factor number .

Step-1: Prime Factorization of 1891

Prime factors of 1891 are 31, 61. Prime factorization of 1891 in exponential form is:

1891 = 31¹ × 61¹

Step-2: Prime Factorization of 1909

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

1909 = 23¹ × 83¹

Step-3: Factors of 1891

List of positive integer factors of 1891 that divides 1891 without a remainder.

1, 31, 61

Step-4: Factors of 1909

List of positive integer factors of 1909 that divides 1891 without a remainder.

1, 23, 83

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1891 and 1909. The biggest common factor number is the GCF number.
So the greatest common factor 1891 and 1909 is 1.

Also check out the Least Common Multiple of 1891 and 1909