What is the Greatest Common Factor of 1738 and 1748?

Greatest common factor (GCF) of 1738 and 1748 is 2.

GCF(1738,1748) = 2

We will now calculate the prime factors of 1738 and 1748, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1738 and 1748.

How to find the GCF of 1738 and 1748?

We will first find the prime factorization of 1738 and 1748. After we will calculate the factors of 1738 and 1748 and find the biggest common factor number .

Step-1: Prime Factorization of 1738

Prime factors of 1738 are 2, 11, 79. Prime factorization of 1738 in exponential form is:

1738 = 2¹ × 11¹ × 79¹

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 1738

List of positive integer factors of 1738 that divides 1738 without a remainder.

1, 2, 11, 22, 79, 158, 869

Step-4: Factors of 1748

List of positive integer factors of 1748 that divides 1738 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 1738 and 1748. The biggest common factor number is the GCF number.
So the greatest common factor 1738 and 1748 is 2.

Also check out the Least Common Multiple of 1738 and 1748