What is the Greatest Common Factor of 20757 and 20774?

Greatest common factor (GCF) of 20757 and 20774 is 17.

GCF(20757,20774) = 17

We will now calculate the prime factors of 20757 and 20774, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20757 and 20774.

How to find the GCF of 20757 and 20774?

We will first find the prime factorization of 20757 and 20774. After we will calculate the factors of 20757 and 20774 and find the biggest common factor number .

Step-1: Prime Factorization of 20757

Prime factors of 20757 are 3, 11, 17, 37. Prime factorization of 20757 in exponential form is:

20757 = 3¹ × 11¹ × 17¹ × 37¹

Step-2: Prime Factorization of 20774

Prime factors of 20774 are 2, 13, 17, 47. Prime factorization of 20774 in exponential form is:

20774 = 2¹ × 13¹ × 17¹ × 47¹

Step-3: Factors of 20757

List of positive integer factors of 20757 that divides 20757 without a remainder.

1, 3, 11, 17, 33, 37, 51, 111, 187, 407, 561, 629, 1221, 1887, 6919

Step-4: Factors of 20774

List of positive integer factors of 20774 that divides 20757 without a remainder.

1, 2, 13, 17, 26, 34, 47, 94, 221, 442, 611, 799, 1222, 1598, 10387

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20757 and 20774. The biggest common factor number is the GCF number.
So the greatest common factor 20757 and 20774 is 17.

Also check out the Least Common Multiple of 20757 and 20774