What is the Greatest Common Factor of 1780 and 1800?

Greatest common factor (GCF) of 1780 and 1800 is 20.

GCF(1780,1800) = 20

We will now calculate the prime factors of 1780 and 1800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1780 and 1800.

How to find the GCF of 1780 and 1800?

We will first find the prime factorization of 1780 and 1800. After we will calculate the factors of 1780 and 1800 and find the biggest common factor number .

Step-1: Prime Factorization of 1780

Prime factors of 1780 are 2, 5, 89. Prime factorization of 1780 in exponential form is:

1780 = 2² × 5¹ × 89¹

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 1780

List of positive integer factors of 1780 that divides 1780 without a remainder.

1, 2, 4, 5, 10, 20, 89, 178, 356, 445, 890

Step-4: Factors of 1800

List of positive integer factors of 1800 that divides 1780 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 1780 and 1800. The biggest common factor number is the GCF number.
So the greatest common factor 1780 and 1800 is 20.

Also check out the Least Common Multiple of 1780 and 1800