What is the Greatest Common Factor of 1738 and 1749?

Greatest common factor (GCF) of 1738 and 1749 is 11.

GCF(1738,1749) = 11

We will now calculate the prime factors of 1738 and 1749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1738 and 1749.

How to find the GCF of 1738 and 1749?

We will first find the prime factorization of 1738 and 1749. After we will calculate the factors of 1738 and 1749 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 1749

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

1749 = 3¹ × 11¹ × 53¹

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 1749

List of positive integer factors of 1749 that divides 1738 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1738 and 1749. The biggest common factor number is the GCF number.
So the greatest common factor 1738 and 1749 is 11.

Also check out the Least Common Multiple of 1738 and 1749