What is the Greatest Common Factor of 26782 and 26800?

Greatest common factor (GCF) of 26782 and 26800 is 2.

GCF(26782,26800) = 2

We will now calculate the prime factors of 26782 and 26800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 26782 and 26800.

How to find the GCF of 26782 and 26800?

We will first find the prime factorization of 26782 and 26800. After we will calculate the factors of 26782 and 26800 and find the biggest common factor number .

Step-1: Prime Factorization of 26782

Prime factors of 26782 are 2, 7, 1913. Prime factorization of 26782 in exponential form is:

26782 = 2¹ × 7¹ × 1913¹

Step-2: Prime Factorization of 26800

Prime factors of 26800 are 2, 5, 67. Prime factorization of 26800 in exponential form is:

26800 = 2⁴ × 5² × 67¹

Step-3: Factors of 26782

List of positive integer factors of 26782 that divides 26782 without a remainder.

1, 2, 7, 14, 1913, 3826, 13391

Step-4: Factors of 26800

List of positive integer factors of 26800 that divides 26782 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 67, 80, 100, 134, 200, 268, 335, 400, 536, 670, 1072, 1340, 1675, 2680, 3350, 5360, 6700, 13400

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 26782 and 26800. The biggest common factor number is the GCF number.
So the greatest common factor 26782 and 26800 is 2.

Also check out the Least Common Multiple of 26782 and 26800