What is the Greatest Common Factor of 17744 and 17762?

Greatest common factor (GCF) of 17744 and 17762 is 2.

GCF(17744,17762) = 2

We will now calculate the prime factors of 17744 and 17762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17744 and 17762.

How to find the GCF of 17744 and 17762?

We will first find the prime factorization of 17744 and 17762. After we will calculate the factors of 17744 and 17762 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 17762

Prime factors of 17762 are 2, 83, 107. Prime factorization of 17762 in exponential form is:

17762 = 2¹ × 83¹ × 107¹

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 17762

List of positive integer factors of 17762 that divides 17744 without a remainder.

1, 2, 83, 107, 166, 214, 8881

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17744 and 17762. The biggest common factor number is the GCF number.
So the greatest common factor 17744 and 17762 is 2.

Also check out the Least Common Multiple of 17744 and 17762