What is the Greatest Common Factor of 34725 and 34730?

Greatest common factor (GCF) of 34725 and 34730 is 5.

GCF(34725,34730) = 5

We will now calculate the prime factors of 34725 and 34730, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34725 and 34730.

How to find the GCF of 34725 and 34730?

We will first find the prime factorization of 34725 and 34730. After we will calculate the factors of 34725 and 34730 and find the biggest common factor number .

Step-1: Prime Factorization of 34725

Prime factors of 34725 are 3, 5, 463. Prime factorization of 34725 in exponential form is:

34725 = 3¹ × 5² × 463¹

Step-2: Prime Factorization of 34730

Prime factors of 34730 are 2, 5, 23, 151. Prime factorization of 34730 in exponential form is:

34730 = 2¹ × 5¹ × 23¹ × 151¹

Step-3: Factors of 34725

List of positive integer factors of 34725 that divides 34725 without a remainder.

1, 3, 5, 15, 25, 75, 463, 1389, 2315, 6945, 11575

Step-4: Factors of 34730

List of positive integer factors of 34730 that divides 34725 without a remainder.

1, 2, 5, 10, 23, 46, 115, 151, 230, 302, 755, 1510, 3473, 6946, 17365

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34725 and 34730. The biggest common factor number is the GCF number.
So the greatest common factor 34725 and 34730 is 5.

Also check out the Least Common Multiple of 34725 and 34730