What is the Greatest Common Factor of 17782 and 17800?

Greatest common factor (GCF) of 17782 and 17800 is 2.

GCF(17782,17800) = 2

We will now calculate the prime factors of 17782 and 17800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17782 and 17800.

How to find the GCF of 17782 and 17800?

We will first find the prime factorization of 17782 and 17800. After we will calculate the factors of 17782 and 17800 and find the biggest common factor number .

Step-1: Prime Factorization of 17782

Prime factors of 17782 are 2, 17, 523. Prime factorization of 17782 in exponential form is:

17782 = 2¹ × 17¹ × 523¹

Step-2: 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-3: Factors of 17782

List of positive integer factors of 17782 that divides 17782 without a remainder.

1, 2, 17, 34, 523, 1046, 8891

Step-4: Factors of 17800

List of positive integer factors of 17800 that divides 17782 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17782 and 17800. The biggest common factor number is the GCF number.
So the greatest common factor 17782 and 17800 is 2.

Also check out the Least Common Multiple of 17782 and 17800