What is the Greatest Common Factor of 1764 and 1784?

Greatest common factor (GCF) of 1764 and 1784 is 4.

GCF(1764,1784) = 4

We will now calculate the prime factors of 1764 and 1784, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1764 and 1784.

How to find the GCF of 1764 and 1784?

We will first find the prime factorization of 1764 and 1784. After we will calculate the factors of 1764 and 1784 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 1784

Prime factors of 1784 are 2, 223. Prime factorization of 1784 in exponential form is:

1784 = 2³ × 223¹

Step-3: Factors of 1764

List of positive integer factors of 1764 that divides 1764 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

Step-4: Factors of 1784

List of positive integer factors of 1784 that divides 1764 without a remainder.

1, 2, 4, 8, 223, 446, 892

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1764 and 1784. The biggest common factor number is the GCF number.
So the greatest common factor 1764 and 1784 is 4.

Also check out the Least Common Multiple of 1764 and 1784