What is the Greatest Common Factor of 17814 and 17830?

Greatest common factor (GCF) of 17814 and 17830 is 2.

GCF(17814,17830) = 2

We will now calculate the prime factors of 17814 and 17830, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17814 and 17830.

How to find the GCF of 17814 and 17830?

We will first find the prime factorization of 17814 and 17830. After we will calculate the factors of 17814 and 17830 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 17830

Prime factors of 17830 are 2, 5, 1783. Prime factorization of 17830 in exponential form is:

17830 = 2¹ × 5¹ × 1783¹

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 17830

List of positive integer factors of 17830 that divides 17814 without a remainder.

1, 2, 5, 10, 1783, 3566, 8915

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17814 and 17830. The biggest common factor number is the GCF number.
So the greatest common factor 17814 and 17830 is 2.

Also check out the Least Common Multiple of 17814 and 17830