What is the Greatest Common Factor of 17748 and 17763?

Greatest common factor (GCF) of 17748 and 17763 is 3.

GCF(17748,17763) = 3

We will now calculate the prime factors of 17748 and 17763, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17748 and 17763.

How to find the GCF of 17748 and 17763?

We will first find the prime factorization of 17748 and 17763. After we will calculate the factors of 17748 and 17763 and find the biggest common factor number .

Step-1: Prime Factorization of 17748

Prime factors of 17748 are 2, 3, 17, 29. Prime factorization of 17748 in exponential form is:

17748 = 2² × 3² × 17¹ × 29¹

Step-2: Prime Factorization of 17763

Prime factors of 17763 are 3, 31, 191. Prime factorization of 17763 in exponential form is:

17763 = 3¹ × 31¹ × 191¹

Step-3: Factors of 17748

List of positive integer factors of 17748 that divides 17748 without a remainder.

1, 2, 3, 4, 6, 9, 12, 17, 18, 29, 34, 36, 51, 58, 68, 87, 102, 116, 153, 174, 204, 261, 306, 348, 493, 522, 612, 986, 1044, 1479, 1972, 2958, 4437, 5916, 8874

Step-4: Factors of 17763

List of positive integer factors of 17763 that divides 17748 without a remainder.

1, 3, 31, 93, 191, 573, 5921

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17748 and 17763. The biggest common factor number is the GCF number.
So the greatest common factor 17748 and 17763 is 3.

Also check out the Least Common Multiple of 17748 and 17763