What is the Greatest Common Factor of 1814 and 1830?

Greatest common factor (GCF) of 1814 and 1830 is 2.

GCF(1814,1830) = 2

We will now calculate the prime factors of 1814 and 1830, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1814 and 1830.

How to find the GCF of 1814 and 1830?

We will first find the prime factorization of 1814 and 1830. After we will calculate the factors of 1814 and 1830 and find the biggest common factor number .

Step-1: Prime Factorization of 1814

Prime factors of 1814 are 2, 907. Prime factorization of 1814 in exponential form is:

1814 = 2¹ × 907¹

Step-2: Prime Factorization of 1830

Prime factors of 1830 are 2, 3, 5, 61. Prime factorization of 1830 in exponential form is:

1830 = 2¹ × 3¹ × 5¹ × 61¹

Step-3: Factors of 1814

List of positive integer factors of 1814 that divides 1814 without a remainder.

1, 2, 907

Step-4: Factors of 1830

List of positive integer factors of 1830 that divides 1814 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 61, 122, 183, 305, 366, 610, 915

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1814 and 1830. The biggest common factor number is the GCF number.
So the greatest common factor 1814 and 1830 is 2.

Also check out the Least Common Multiple of 1814 and 1830