What is the Greatest Common Factor of 51825 and 51834?

Greatest common factor (GCF) of 51825 and 51834 is 3.

GCF(51825,51834) = 3

We will now calculate the prime factors of 51825 and 51834, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51825 and 51834.

How to find the GCF of 51825 and 51834?

We will first find the prime factorization of 51825 and 51834. After we will calculate the factors of 51825 and 51834 and find the biggest common factor number .

Step-1: Prime Factorization of 51825

Prime factors of 51825 are 3, 5, 691. Prime factorization of 51825 in exponential form is:

51825 = 3¹ × 5² × 691¹

Step-2: Prime Factorization of 51834

Prime factors of 51834 are 2, 3, 53, 163. Prime factorization of 51834 in exponential form is:

51834 = 2¹ × 3¹ × 53¹ × 163¹

Step-3: Factors of 51825

List of positive integer factors of 51825 that divides 51825 without a remainder.

1, 3, 5, 15, 25, 75, 691, 2073, 3455, 10365, 17275

Step-4: Factors of 51834

List of positive integer factors of 51834 that divides 51825 without a remainder.

1, 2, 3, 6, 53, 106, 159, 163, 318, 326, 489, 978, 8639, 17278, 25917

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51825 and 51834. The biggest common factor number is the GCF number.
So the greatest common factor 51825 and 51834 is 3.

Also check out the Least Common Multiple of 51825 and 51834