What is the Greatest Common Factor of 705 and 719?

Greatest common factor (GCF) of 705 and 719 is 1.

GCF(705,719) = 1

We will now calculate the prime factors of 705 and 719, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 705 and 719.

How to find the GCF of 705 and 719?

We will first find the prime factorization of 705 and 719. After we will calculate the factors of 705 and 719 and find the biggest common factor number .

Step-1: Prime Factorization of 705

Prime factors of 705 are 3, 5, 47. Prime factorization of 705 in exponential form is:

705 = 3¹ × 5¹ × 47¹

Step-2: Prime Factorization of 719

Prime factors of 719 are 719. Prime factorization of 719 in exponential form is:

719 = 719¹

Step-3: Factors of 705

List of positive integer factors of 705 that divides 705 without a remainder.

1, 3, 5, 15, 47, 141, 235

Step-4: Factors of 719

List of positive integer factors of 719 that divides 705 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 705 and 719. The biggest common factor number is the GCF number.
So the greatest common factor 705 and 719 is 1.

Also check out the Least Common Multiple of 705 and 719