What is the Greatest Common Factor of 705 and 721?

Greatest common factor (GCF) of 705 and 721 is 1.

GCF(705,721) = 1

We will now calculate the prime factors of 705 and 721, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 705 and 721.

How to find the GCF of 705 and 721?

We will first find the prime factorization of 705 and 721. After we will calculate the factors of 705 and 721 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 721

Prime factors of 721 are 7, 103. Prime factorization of 721 in exponential form is:

721 = 7¹ × 103¹

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 721

List of positive integer factors of 721 that divides 705 without a remainder.

1, 7, 103

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 705 and 721. The biggest common factor number is the GCF number.
So the greatest common factor 705 and 721 is 1.

Also check out the Least Common Multiple of 705 and 721