What is the Greatest Common Factor of 20742 and 20757?

Greatest common factor (GCF) of 20742 and 20757 is 3.

GCF(20742,20757) = 3

We will now calculate the prime factors of 20742 and 20757, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20742 and 20757.

How to find the GCF of 20742 and 20757?

We will first find the prime factorization of 20742 and 20757. After we will calculate the factors of 20742 and 20757 and find the biggest common factor number .

Step-1: Prime Factorization of 20742

Prime factors of 20742 are 2, 3, 3457. Prime factorization of 20742 in exponential form is:

20742 = 2¹ × 3¹ × 3457¹

Step-2: 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-3: Factors of 20742

List of positive integer factors of 20742 that divides 20742 without a remainder.

1, 2, 3, 6, 3457, 6914, 10371

Step-4: Factors of 20757

List of positive integer factors of 20757 that divides 20742 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20742 and 20757. The biggest common factor number is the GCF number.
So the greatest common factor 20742 and 20757 is 3.

Also check out the Least Common Multiple of 20742 and 20757