What is the Greatest Common Factor of 75705 and 75723?

Greatest common factor (GCF) of 75705 and 75723 is 3.

GCF(75705,75723) = 3

We will now calculate the prime factors of 75705 and 75723, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75705 and 75723.

How to find the GCF of 75705 and 75723?

We will first find the prime factorization of 75705 and 75723. After we will calculate the factors of 75705 and 75723 and find the biggest common factor number .

Step-1: Prime Factorization of 75705

Prime factors of 75705 are 3, 5, 7, 103. Prime factorization of 75705 in exponential form is:

75705 = 3¹ × 5¹ × 7² × 103¹

Step-2: Prime Factorization of 75723

Prime factors of 75723 are 3, 43, 587. Prime factorization of 75723 in exponential form is:

75723 = 3¹ × 43¹ × 587¹

Step-3: Factors of 75705

List of positive integer factors of 75705 that divides 75705 without a remainder.

1, 3, 5, 7, 15, 21, 35, 49, 103, 105, 147, 245, 309, 515, 721, 735, 1545, 2163, 3605, 5047, 10815, 15141, 25235

Step-4: Factors of 75723

List of positive integer factors of 75723 that divides 75705 without a remainder.

1, 3, 43, 129, 587, 1761, 25241

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75705 and 75723. The biggest common factor number is the GCF number.
So the greatest common factor 75705 and 75723 is 3.

Also check out the Least Common Multiple of 75705 and 75723