What is the Greatest Common Factor of 1744 and 1754?

Greatest common factor (GCF) of 1744 and 1754 is 2.

GCF(1744,1754) = 2

We will now calculate the prime factors of 1744 and 1754, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1744 and 1754.

How to find the GCF of 1744 and 1754?

We will first find the prime factorization of 1744 and 1754. After we will calculate the factors of 1744 and 1754 and find the biggest common factor number .

Step-1: Prime Factorization of 1744

Prime factors of 1744 are 2, 109. Prime factorization of 1744 in exponential form is:

1744 = 2⁴ × 109¹

Step-2: Prime Factorization of 1754

Prime factors of 1754 are 2, 877. Prime factorization of 1754 in exponential form is:

1754 = 2¹ × 877¹

Step-3: Factors of 1744

List of positive integer factors of 1744 that divides 1744 without a remainder.

1, 2, 4, 8, 16, 109, 218, 436, 872

Step-4: Factors of 1754

List of positive integer factors of 1754 that divides 1744 without a remainder.

1, 2, 877

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1744 and 1754. The biggest common factor number is the GCF number.
So the greatest common factor 1744 and 1754 is 2.

Also check out the Least Common Multiple of 1744 and 1754