What is the Greatest Common Factor of 27825 and 27834?

Greatest common factor (GCF) of 27825 and 27834 is 3.

GCF(27825,27834) = 3

We will now calculate the prime factors of 27825 and 27834, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27825 and 27834.

How to find the GCF of 27825 and 27834?

We will first find the prime factorization of 27825 and 27834. After we will calculate the factors of 27825 and 27834 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 27834

Prime factors of 27834 are 2, 3, 4639. Prime factorization of 27834 in exponential form is:

27834 = 2¹ × 3¹ × 4639¹

Step-3: Factors of 27825

List of positive integer factors of 27825 that divides 27825 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

Step-4: Factors of 27834

List of positive integer factors of 27834 that divides 27825 without a remainder.

1, 2, 3, 6, 4639, 9278, 13917

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27825 and 27834. The biggest common factor number is the GCF number.
So the greatest common factor 27825 and 27834 is 3.

Also check out the Least Common Multiple of 27825 and 27834