What is the Greatest Common Factor of 1768 and 1782?

Greatest common factor (GCF) of 1768 and 1782 is 2.

GCF(1768,1782) = 2

We will now calculate the prime factors of 1768 and 1782, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1768 and 1782.

How to find the GCF of 1768 and 1782?

We will first find the prime factorization of 1768 and 1782. After we will calculate the factors of 1768 and 1782 and find the biggest common factor number .

Step-1: Prime Factorization of 1768

Prime factors of 1768 are 2, 13, 17. Prime factorization of 1768 in exponential form is:

1768 = 2³ × 13¹ × 17¹

Step-2: 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-3: Factors of 1768

List of positive integer factors of 1768 that divides 1768 without a remainder.

1, 2, 4, 8, 13, 17, 26, 34, 52, 68, 104, 136, 221, 442, 884

Step-4: Factors of 1782

List of positive integer factors of 1782 that divides 1768 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1768 and 1782. The biggest common factor number is the GCF number.
So the greatest common factor 1768 and 1782 is 2.

Also check out the Least Common Multiple of 1768 and 1782