What is the Greatest Common Factor of 75705 and 75725?

Greatest common factor (GCF) of 75705 and 75725 is 5.

GCF(75705,75725) = 5

We will now calculate the prime factors of 75705 and 75725, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75705 and 75725.

How to find the GCF of 75705 and 75725?

We will first find the prime factorization of 75705 and 75725. After we will calculate the factors of 75705 and 75725 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 75725

Prime factors of 75725 are 5, 13, 233. Prime factorization of 75725 in exponential form is:

75725 = 5² × 13¹ × 233¹

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 75725

List of positive integer factors of 75725 that divides 75705 without a remainder.

1, 5, 13, 25, 65, 233, 325, 1165, 3029, 5825, 15145

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75705 and 75725. The biggest common factor number is the GCF number.
So the greatest common factor 75705 and 75725 is 5.

Also check out the Least Common Multiple of 75705 and 75725