What is the Greatest Common Factor of 27805 and 27825?

Greatest common factor (GCF) of 27805 and 27825 is 5.

GCF(27805,27825) = 5

We will now calculate the prime factors of 27805 and 27825, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27805 and 27825.

How to find the GCF of 27805 and 27825?

We will first find the prime factorization of 27805 and 27825. After we will calculate the factors of 27805 and 27825 and find the biggest common factor number .

Step-1: Prime Factorization of 27805

Prime factors of 27805 are 5, 67, 83. Prime factorization of 27805 in exponential form is:

27805 = 5¹ × 67¹ × 83¹

Step-2: Prime Factorization of 27825

Prime factors of 27825 are 3, 5, 7, 53. Prime factorization of 27825 in exponential form is:

27825 = 3¹ × 5² × 7¹ × 53¹

Step-3: Factors of 27805

List of positive integer factors of 27805 that divides 27805 without a remainder.

1, 5, 67, 83, 335, 415, 5561

Step-4: Factors of 27825

List of positive integer factors of 27825 that divides 27805 without a remainder.

1, 3, 5, 7, 15, 21, 25, 35, 53, 75, 105, 159, 175, 265, 371, 525, 795, 1113, 1325, 1855, 3975, 5565, 9275

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27805 and 27825. The biggest common factor number is the GCF number.
So the greatest common factor 27805 and 27825 is 5.

Also check out the Least Common Multiple of 27805 and 27825