What is the Greatest Common Factor of 17744 and 17749?

Greatest common factor (GCF) of 17744 and 17749 is 1.

GCF(17744,17749) = 1

We will now calculate the prime factors of 17744 and 17749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17744 and 17749.

How to find the GCF of 17744 and 17749?

We will first find the prime factorization of 17744 and 17749. After we will calculate the factors of 17744 and 17749 and find the biggest common factor number .

Step-1: Prime Factorization of 17744

Prime factors of 17744 are 2, 1109. Prime factorization of 17744 in exponential form is:

17744 = 2⁴ × 1109¹

Step-2: Prime Factorization of 17749

Prime factors of 17749 are 17749. Prime factorization of 17749 in exponential form is:

17749 = 17749¹

Step-3: Factors of 17744

List of positive integer factors of 17744 that divides 17744 without a remainder.

1, 2, 4, 8, 16, 1109, 2218, 4436, 8872

Step-4: Factors of 17749

List of positive integer factors of 17749 that divides 17744 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17744 and 17749. The biggest common factor number is the GCF number.
So the greatest common factor 17744 and 17749 is 1.

Also check out the Least Common Multiple of 17744 and 17749