What is the Greatest Common Factor of 5705 and 5719?

Greatest common factor (GCF) of 5705 and 5719 is 7.

GCF(5705,5719) = 7

We will now calculate the prime factors of 5705 and 5719, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5705 and 5719.

How to find the GCF of 5705 and 5719?

We will first find the prime factorization of 5705 and 5719. After we will calculate the factors of 5705 and 5719 and find the biggest common factor number .

Step-1: Prime Factorization of 5705

Prime factors of 5705 are 5, 7, 163. Prime factorization of 5705 in exponential form is:

5705 = 5¹ × 7¹ × 163¹

Step-2: Prime Factorization of 5719

Prime factors of 5719 are 7, 19, 43. Prime factorization of 5719 in exponential form is:

5719 = 7¹ × 19¹ × 43¹

Step-3: Factors of 5705

List of positive integer factors of 5705 that divides 5705 without a remainder.

1, 5, 7, 35, 163, 815, 1141

Step-4: Factors of 5719

List of positive integer factors of 5719 that divides 5705 without a remainder.

1, 7, 19, 43, 133, 301, 817

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5705 and 5719. The biggest common factor number is the GCF number.
So the greatest common factor 5705 and 5719 is 7.

Also check out the Least Common Multiple of 5705 and 5719