What is the Greatest Common Factor of 20706 and 20723?

Greatest common factor (GCF) of 20706 and 20723 is 17.

GCF(20706,20723) = 17

We will now calculate the prime factors of 20706 and 20723, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20706 and 20723.

How to find the GCF of 20706 and 20723?

We will first find the prime factorization of 20706 and 20723. After we will calculate the factors of 20706 and 20723 and find the biggest common factor number .

Step-1: Prime Factorization of 20706

Prime factors of 20706 are 2, 3, 7, 17, 29. Prime factorization of 20706 in exponential form is:

20706 = 2¹ × 3¹ × 7¹ × 17¹ × 29¹

Step-2: Prime Factorization of 20723

Prime factors of 20723 are 17, 23, 53. Prime factorization of 20723 in exponential form is:

20723 = 17¹ × 23¹ × 53¹

Step-3: Factors of 20706

List of positive integer factors of 20706 that divides 20706 without a remainder.

1, 2, 3, 6, 7, 14, 17, 21, 29, 34, 42, 51, 58, 87, 102, 119, 174, 203, 238, 357, 406, 493, 609, 714, 986, 1218, 1479, 2958, 3451, 6902, 10353

Step-4: Factors of 20723

List of positive integer factors of 20723 that divides 20706 without a remainder.

1, 17, 23, 53, 391, 901, 1219

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20706 and 20723. The biggest common factor number is the GCF number.
So the greatest common factor 20706 and 20723 is 17.

Also check out the Least Common Multiple of 20706 and 20723