What is the Greatest Common Factor of 26705 and 26719?

Greatest common factor (GCF) of 26705 and 26719 is 7.

GCF(26705,26719) = 7

We will now calculate the prime factors of 26705 and 26719, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 26705 and 26719.

How to find the GCF of 26705 and 26719?

We will first find the prime factorization of 26705 and 26719. After we will calculate the factors of 26705 and 26719 and find the biggest common factor number .

Step-1: Prime Factorization of 26705

Prime factors of 26705 are 5, 7, 109. Prime factorization of 26705 in exponential form is:

26705 = 5¹ × 7² × 109¹

Step-2: Prime Factorization of 26719

Prime factors of 26719 are 7, 11, 347. Prime factorization of 26719 in exponential form is:

26719 = 7¹ × 11¹ × 347¹

Step-3: Factors of 26705

List of positive integer factors of 26705 that divides 26705 without a remainder.

1, 5, 7, 35, 49, 109, 245, 545, 763, 3815, 5341

Step-4: Factors of 26719

List of positive integer factors of 26719 that divides 26705 without a remainder.

1, 7, 11, 77, 347, 2429, 3817

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 26705 and 26719. The biggest common factor number is the GCF number.
So the greatest common factor 26705 and 26719 is 7.

Also check out the Least Common Multiple of 26705 and 26719