What is the Greatest Common Factor of 1782 and 1800?

Greatest common factor (GCF) of 1782 and 1800 is 18.

GCF(1782,1800) = 18

We will now calculate the prime factors of 1782 and 1800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1782 and 1800.

How to find the GCF of 1782 and 1800?

We will first find the prime factorization of 1782 and 1800. After we will calculate the factors of 1782 and 1800 and find the biggest common factor number .

Step-1: Prime Factorization of 1782

Prime factors of 1782 are 2, 3, 11. Prime factorization of 1782 in exponential form is:

1782 = 2¹ × 3⁴ × 11¹

Step-2: Prime Factorization of 1800

Prime factors of 1800 are 2, 3, 5. Prime factorization of 1800 in exponential form is:

1800 = 2³ × 3² × 5²

Step-3: Factors of 1782

List of positive integer factors of 1782 that divides 1782 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 27, 33, 54, 66, 81, 99, 162, 198, 297, 594, 891

Step-4: Factors of 1800

List of positive integer factors of 1800 that divides 1782 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 150, 180, 200, 225, 300, 360, 450, 600, 900

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1782 and 1800. The biggest common factor number is the GCF number.
So the greatest common factor 1782 and 1800 is 18.

Also check out the Least Common Multiple of 1782 and 1800