What is the Greatest Common Factor of 1827 and 1834?

Greatest common factor (GCF) of 1827 and 1834 is 7.

GCF(1827,1834) = 7

We will now calculate the prime factors of 1827 and 1834, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1827 and 1834.

How to find the GCF of 1827 and 1834?

We will first find the prime factorization of 1827 and 1834. After we will calculate the factors of 1827 and 1834 and find the biggest common factor number .

Step-1: Prime Factorization of 1827

Prime factors of 1827 are 3, 7, 29. Prime factorization of 1827 in exponential form is:

1827 = 3² × 7¹ × 29¹

Step-2: Prime Factorization of 1834

Prime factors of 1834 are 2, 7, 131. Prime factorization of 1834 in exponential form is:

1834 = 2¹ × 7¹ × 131¹

Step-3: Factors of 1827

List of positive integer factors of 1827 that divides 1827 without a remainder.

1, 3, 7, 9, 21, 29, 63, 87, 203, 261, 609

Step-4: Factors of 1834

List of positive integer factors of 1834 that divides 1827 without a remainder.

1, 2, 7, 14, 131, 262, 917

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1827 and 1834. The biggest common factor number is the GCF number.
So the greatest common factor 1827 and 1834 is 7.

Also check out the Least Common Multiple of 1827 and 1834