What is the Greatest Common Factor of 1782 and 1802?

Greatest common factor (GCF) of 1782 and 1802 is 2.

GCF(1782,1802) = 2

We will now calculate the prime factors of 1782 and 1802, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1782 and 1802.

How to find the GCF of 1782 and 1802?

We will first find the prime factorization of 1782 and 1802. After we will calculate the factors of 1782 and 1802 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 1802

Prime factors of 1802 are 2, 17, 53. Prime factorization of 1802 in exponential form is:

1802 = 2¹ × 17¹ × 53¹

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 1802

List of positive integer factors of 1802 that divides 1782 without a remainder.

1, 2, 17, 34, 53, 106, 901

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1782 and 1802. The biggest common factor number is the GCF number.
So the greatest common factor 1782 and 1802 is 2.

Also check out the Least Common Multiple of 1782 and 1802