What is the Greatest Common Factor of 75705 and 75709?

Greatest common factor (GCF) of 75705 and 75709 is 1.

GCF(75705,75709) = 1

We will now calculate the prime factors of 75705 and 75709, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75705 and 75709.

How to find the GCF of 75705 and 75709?

We will first find the prime factorization of 75705 and 75709. After we will calculate the factors of 75705 and 75709 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 75709

Prime factors of 75709 are 75709. Prime factorization of 75709 in exponential form is:

75709 = 75709¹

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 75709

List of positive integer factors of 75709 that divides 75705 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75705 and 75709. The biggest common factor number is the GCF number.
So the greatest common factor 75705 and 75709 is 1.

Also check out the Least Common Multiple of 75705 and 75709