What is the Greatest Common Factor of 1749 and 1758?

Greatest common factor (GCF) of 1749 and 1758 is 3.

GCF(1749,1758) = 3

We will now calculate the prime factors of 1749 and 1758, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1749 and 1758.

How to find the GCF of 1749 and 1758?

We will first find the prime factorization of 1749 and 1758. After we will calculate the factors of 1749 and 1758 and find the biggest common factor number .

Step-1: Prime Factorization of 1749

Prime factors of 1749 are 3, 11, 53. Prime factorization of 1749 in exponential form is:

1749 = 3¹ × 11¹ × 53¹

Step-2: Prime Factorization of 1758

Prime factors of 1758 are 2, 3, 293. Prime factorization of 1758 in exponential form is:

1758 = 2¹ × 3¹ × 293¹

Step-3: Factors of 1749

List of positive integer factors of 1749 that divides 1749 without a remainder.

1, 3, 11, 33, 53, 159, 583

Step-4: Factors of 1758

List of positive integer factors of 1758 that divides 1749 without a remainder.

1, 2, 3, 6, 293, 586, 879

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1749 and 1758. The biggest common factor number is the GCF number.
So the greatest common factor 1749 and 1758 is 3.

Also check out the Least Common Multiple of 1749 and 1758