What is the Greatest Common Factor of 21736 and 21749?

Greatest common factor (GCF) of 21736 and 21749 is 13.

GCF(21736,21749) = 13

We will now calculate the prime factors of 21736 and 21749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21736 and 21749.

How to find the GCF of 21736 and 21749?

We will first find the prime factorization of 21736 and 21749. After we will calculate the factors of 21736 and 21749 and find the biggest common factor number .

Step-1: Prime Factorization of 21736

Prime factors of 21736 are 2, 11, 13, 19. Prime factorization of 21736 in exponential form is:

21736 = 2³ × 11¹ × 13¹ × 19¹

Step-2: 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-3: Factors of 21736

List of positive integer factors of 21736 that divides 21736 without a remainder.

1, 2, 4, 8, 11, 13, 19, 22, 26, 38, 44, 52, 76, 88, 104, 143, 152, 209, 247, 286, 418, 494, 572, 836, 988, 1144, 1672, 1976, 2717, 5434, 10868

Step-4: Factors of 21749

List of positive integer factors of 21749 that divides 21736 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21736 and 21749. The biggest common factor number is the GCF number.
So the greatest common factor 21736 and 21749 is 13.

Also check out the Least Common Multiple of 21736 and 21749