What is the Greatest Common Factor of 1729 and 1748?

Greatest common factor (GCF) of 1729 and 1748 is 19.

GCF(1729,1748) = 19

We will now calculate the prime factors of 1729 and 1748, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1729 and 1748.

How to find the GCF of 1729 and 1748?

We will first find the prime factorization of 1729 and 1748. After we will calculate the factors of 1729 and 1748 and find the biggest common factor number .

Step-1: Prime Factorization of 1729

Prime factors of 1729 are 7, 13, 19. Prime factorization of 1729 in exponential form is:

1729 = 7¹ × 13¹ × 19¹

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 1729

List of positive integer factors of 1729 that divides 1729 without a remainder.

1, 7, 13, 19, 91, 133, 247

Step-4: Factors of 1748

List of positive integer factors of 1748 that divides 1729 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 1729 and 1748. The biggest common factor number is the GCF number.
So the greatest common factor 1729 and 1748 is 19.

Also check out the Least Common Multiple of 1729 and 1748