What is the Greatest Common Factor of 1764 and 1776?

Greatest common factor (GCF) of 1764 and 1776 is 12.

GCF(1764,1776) = 12

We will now calculate the prime factors of 1764 and 1776, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1764 and 1776.

How to find the GCF of 1764 and 1776?

We will first find the prime factorization of 1764 and 1776. After we will calculate the factors of 1764 and 1776 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 1776

Prime factors of 1776 are 2, 3, 37. Prime factorization of 1776 in exponential form is:

1776 = 2⁴ × 3¹ × 37¹

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 1776

List of positive integer factors of 1776 that divides 1764 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 37, 48, 74, 111, 148, 222, 296, 444, 592, 888

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1764 and 1776. The biggest common factor number is the GCF number.
So the greatest common factor 1764 and 1776 is 12.

Also check out the Least Common Multiple of 1764 and 1776