What is the Greatest Common Factor of 705 and 724?

Greatest common factor (GCF) of 705 and 724 is 1.

GCF(705,724) = 1

We will now calculate the prime factors of 705 and 724, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 705 and 724.

How to find the GCF of 705 and 724?

We will first find the prime factorization of 705 and 724. After we will calculate the factors of 705 and 724 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 724

Prime factors of 724 are 2, 181. Prime factorization of 724 in exponential form is:

724 = 2² × 181¹

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 724

List of positive integer factors of 724 that divides 705 without a remainder.

1, 2, 4, 181, 362

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 705 and 724. The biggest common factor number is the GCF number.
So the greatest common factor 705 and 724 is 1.

Also check out the Least Common Multiple of 705 and 724