What is the Greatest Common Factor of 21749 and 21763?

Greatest common factor (GCF) of 21749 and 21763 is 7.

GCF(21749,21763) = 7

We will now calculate the prime factors of 21749 and 21763, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21749 and 21763.

How to find the GCF of 21749 and 21763?

We will first find the prime factorization of 21749 and 21763. After we will calculate the factors of 21749 and 21763 and find the biggest common factor number .

Step-1: Prime Factorization of 21749

Prime factors of 21749 are 7, 13, 239. Prime factorization of 21749 in exponential form is:

21749 = 7¹ × 13¹ × 239¹

Step-2: Prime Factorization of 21763

Prime factors of 21763 are 7, 3109. Prime factorization of 21763 in exponential form is:

21763 = 7¹ × 3109¹

Step-3: Factors of 21749

List of positive integer factors of 21749 that divides 21749 without a remainder.

1, 7, 13, 91, 239, 1673, 3107

Step-4: Factors of 21763

List of positive integer factors of 21763 that divides 21749 without a remainder.

1, 7, 3109

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21749 and 21763. The biggest common factor number is the GCF number.
So the greatest common factor 21749 and 21763 is 7.

Also check out the Least Common Multiple of 21749 and 21763