What is the Greatest Common Factor of 1746 and 1764?

Greatest common factor (GCF) of 1746 and 1764 is 18.

GCF(1746,1764) = 18

We will now calculate the prime factors of 1746 and 1764, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1746 and 1764.

How to find the GCF of 1746 and 1764?

We will first find the prime factorization of 1746 and 1764. After we will calculate the factors of 1746 and 1764 and find the biggest common factor number .

Step-1: Prime Factorization of 1746

Prime factors of 1746 are 2, 3, 97. Prime factorization of 1746 in exponential form is:

1746 = 2¹ × 3² × 97¹

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 1746

List of positive integer factors of 1746 that divides 1746 without a remainder.

1, 2, 3, 6, 9, 18, 97, 194, 291, 582, 873

Step-4: Factors of 1764

List of positive integer factors of 1764 that divides 1746 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 1746 and 1764. The biggest common factor number is the GCF number.
So the greatest common factor 1746 and 1764 is 18.

Also check out the Least Common Multiple of 1746 and 1764