What is the Greatest Common Factor of 1792 and 1806?

Greatest common factor (GCF) of 1792 and 1806 is 14.

GCF(1792,1806) = 14

We will now calculate the prime factors of 1792 and 1806, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1792 and 1806.

How to find the GCF of 1792 and 1806?

We will first find the prime factorization of 1792 and 1806. After we will calculate the factors of 1792 and 1806 and find the biggest common factor number .

Step-1: Prime Factorization of 1792

Prime factors of 1792 are 2, 7. Prime factorization of 1792 in exponential form is:

1792 = 2⁸ × 7¹

Step-2: Prime Factorization of 1806

Prime factors of 1806 are 2, 3, 7, 43. Prime factorization of 1806 in exponential form is:

1806 = 2¹ × 3¹ × 7¹ × 43¹

Step-3: Factors of 1792

List of positive integer factors of 1792 that divides 1792 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 896

Step-4: Factors of 1806

List of positive integer factors of 1806 that divides 1792 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 43, 86, 129, 258, 301, 602, 903

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1792 and 1806. The biggest common factor number is the GCF number.
So the greatest common factor 1792 and 1806 is 14.

Also check out the Least Common Multiple of 1792 and 1806