What is the Greatest Common Factor of 17800 and 17820?

Greatest common factor (GCF) of 17800 and 17820 is 20.

GCF(17800,17820) = 20

We will now calculate the prime factors of 17800 and 17820, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17800 and 17820.

How to find the GCF of 17800 and 17820?

We will first find the prime factorization of 17800 and 17820. After we will calculate the factors of 17800 and 17820 and find the biggest common factor number .

Step-1: Prime Factorization of 17800

Prime factors of 17800 are 2, 5, 89. Prime factorization of 17800 in exponential form is:

17800 = 2³ × 5² × 89¹

Step-2: Prime Factorization of 17820

Prime factors of 17820 are 2, 3, 5, 11. Prime factorization of 17820 in exponential form is:

17820 = 2² × 3⁴ × 5¹ × 11¹

Step-3: Factors of 17800

List of positive integer factors of 17800 that divides 17800 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 89, 100, 178, 200, 356, 445, 712, 890, 1780, 2225, 3560, 4450, 8900

Step-4: Factors of 17820

List of positive integer factors of 17820 that divides 17800 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 27, 30, 33, 36, 44, 45, 54, 55, 60, 66, 81, 90, 99, 108, 110, 132, 135, 162, 165, 180, 198, 220, 270, 297, 324, 330, 396, 405, 495, 540, 594, 660, 810, 891, 990, 1188, 1485, 1620, 1782, 1980, 2970, 3564, 4455, 5940, 8910

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17800 and 17820. The biggest common factor number is the GCF number.
So the greatest common factor 17800 and 17820 is 20.

Also check out the Least Common Multiple of 17800 and 17820