What is the Greatest Common Factor of 17822 and 17834?

Greatest common factor (GCF) of 17822 and 17834 is 2.

GCF(17822,17834) = 2

We will now calculate the prime factors of 17822 and 17834, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17822 and 17834.

How to find the GCF of 17822 and 17834?

We will first find the prime factorization of 17822 and 17834. After we will calculate the factors of 17822 and 17834 and find the biggest common factor number .

Step-1: Prime Factorization of 17822

Prime factors of 17822 are 2, 7, 19, 67. Prime factorization of 17822 in exponential form is:

17822 = 2¹ × 7¹ × 19¹ × 67¹

Step-2: Prime Factorization of 17834

Prime factors of 17834 are 2, 37, 241. Prime factorization of 17834 in exponential form is:

17834 = 2¹ × 37¹ × 241¹

Step-3: Factors of 17822

List of positive integer factors of 17822 that divides 17822 without a remainder.

1, 2, 7, 14, 19, 38, 67, 133, 134, 266, 469, 938, 1273, 2546, 8911

Step-4: Factors of 17834

List of positive integer factors of 17834 that divides 17822 without a remainder.

1, 2, 37, 74, 241, 482, 8917

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17822 and 17834. The biggest common factor number is the GCF number.
So the greatest common factor 17822 and 17834 is 2.

Also check out the Least Common Multiple of 17822 and 17834