What is the Greatest Common Factor of 1734 and 1748?

Greatest common factor (GCF) of 1734 and 1748 is 2.

GCF(1734,1748) = 2

We will now calculate the prime factors of 1734 and 1748, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1734 and 1748.

How to find the GCF of 1734 and 1748?

We will first find the prime factorization of 1734 and 1748. After we will calculate the factors of 1734 and 1748 and find the biggest common factor number .

Step-1: Prime Factorization of 1734

Prime factors of 1734 are 2, 3, 17. Prime factorization of 1734 in exponential form is:

1734 = 2¹ × 3¹ × 17²

Step-2: Prime Factorization of 1748

Prime factors of 1748 are 2, 19, 23. Prime factorization of 1748 in exponential form is:

1748 = 2² × 19¹ × 23¹

Step-3: Factors of 1734

List of positive integer factors of 1734 that divides 1734 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 289, 578, 867

Step-4: Factors of 1748

List of positive integer factors of 1748 that divides 1734 without a remainder.

1, 2, 4, 19, 23, 38, 46, 76, 92, 437, 874

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1734 and 1748. The biggest common factor number is the GCF number.
So the greatest common factor 1734 and 1748 is 2.

Also check out the Least Common Multiple of 1734 and 1748