What is the Greatest Common Factor of 17814 and 17822?

Greatest common factor (GCF) of 17814 and 17822 is 2.

GCF(17814,17822) = 2

We will now calculate the prime factors of 17814 and 17822, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17814 and 17822.

How to find the GCF of 17814 and 17822?

We will first find the prime factorization of 17814 and 17822. After we will calculate the factors of 17814 and 17822 and find the biggest common factor number .

Step-1: Prime Factorization of 17814

Prime factors of 17814 are 2, 3, 2969. Prime factorization of 17814 in exponential form is:

17814 = 2¹ × 3¹ × 2969¹

Step-2: 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-3: Factors of 17814

List of positive integer factors of 17814 that divides 17814 without a remainder.

1, 2, 3, 6, 2969, 5938, 8907

Step-4: Factors of 17822

List of positive integer factors of 17822 that divides 17814 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17814 and 17822. The biggest common factor number is the GCF number.
So the greatest common factor 17814 and 17822 is 2.

Also check out the Least Common Multiple of 17814 and 17822