What is the Greatest Common Factor of 17836 and 17854?

Greatest common factor (GCF) of 17836 and 17854 is 2.

GCF(17836,17854) = 2

We will now calculate the prime factors of 17836 and 17854, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17836 and 17854.

How to find the GCF of 17836 and 17854?

We will first find the prime factorization of 17836 and 17854. After we will calculate the factors of 17836 and 17854 and find the biggest common factor number .

Step-1: Prime Factorization of 17836

Prime factors of 17836 are 2, 7, 13. Prime factorization of 17836 in exponential form is:

17836 = 2² × 7³ × 13¹

Step-2: Prime Factorization of 17854

Prime factors of 17854 are 2, 79, 113. Prime factorization of 17854 in exponential form is:

17854 = 2¹ × 79¹ × 113¹

Step-3: Factors of 17836

List of positive integer factors of 17836 that divides 17836 without a remainder.

1, 2, 4, 7, 13, 14, 26, 28, 49, 52, 91, 98, 182, 196, 343, 364, 637, 686, 1274, 1372, 2548, 4459, 8918

Step-4: Factors of 17854

List of positive integer factors of 17854 that divides 17836 without a remainder.

1, 2, 79, 113, 158, 226, 8927

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17836 and 17854. The biggest common factor number is the GCF number.
So the greatest common factor 17836 and 17854 is 2.

Also check out the Least Common Multiple of 17836 and 17854