What is the Greatest Common Factor of 15827 and 15834?

Greatest common factor (GCF) of 15827 and 15834 is 7.

GCF(15827,15834) = 7

We will now calculate the prime factors of 15827 and 15834, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15827 and 15834.

How to find the GCF of 15827 and 15834?

We will first find the prime factorization of 15827 and 15834. After we will calculate the factors of 15827 and 15834 and find the biggest common factor number .

Step-1: Prime Factorization of 15827

Prime factors of 15827 are 7, 17, 19. Prime factorization of 15827 in exponential form is:

15827 = 7² × 17¹ × 19¹

Step-2: Prime Factorization of 15834

Prime factors of 15834 are 2, 3, 7, 13, 29. Prime factorization of 15834 in exponential form is:

15834 = 2¹ × 3¹ × 7¹ × 13¹ × 29¹

Step-3: Factors of 15827

List of positive integer factors of 15827 that divides 15827 without a remainder.

1, 7, 17, 19, 49, 119, 133, 323, 833, 931, 2261

Step-4: Factors of 15834

List of positive integer factors of 15834 that divides 15827 without a remainder.

1, 2, 3, 6, 7, 13, 14, 21, 26, 29, 39, 42, 58, 78, 87, 91, 174, 182, 203, 273, 377, 406, 546, 609, 754, 1131, 1218, 2262, 2639, 5278, 7917

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15827 and 15834. The biggest common factor number is the GCF number.
So the greatest common factor 15827 and 15834 is 7.

Also check out the Least Common Multiple of 15827 and 15834