What is the Greatest Common Factor of 1749 and 1764?

Greatest common factor (GCF) of 1749 and 1764 is 3.

GCF(1749,1764) = 3

We will now calculate the prime factors of 1749 and 1764, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1749 and 1764.

How to find the GCF of 1749 and 1764?

We will first find the prime factorization of 1749 and 1764. After we will calculate the factors of 1749 and 1764 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 1764

Prime factors of 1764 are 2, 3, 7. Prime factorization of 1764 in exponential form is:

1764 = 2² × 3² × 7²

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 1764

List of positive integer factors of 1764 that divides 1749 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1749 and 1764. The biggest common factor number is the GCF number.
So the greatest common factor 1749 and 1764 is 3.

Also check out the Least Common Multiple of 1749 and 1764