What is the Greatest Common Factor of 1764 and 1778?

Greatest common factor (GCF) of 1764 and 1778 is 14.

GCF(1764,1778) = 14

We will now calculate the prime factors of 1764 and 1778, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1764 and 1778.

How to find the GCF of 1764 and 1778?

We will first find the prime factorization of 1764 and 1778. After we will calculate the factors of 1764 and 1778 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 1778

Prime factors of 1778 are 2, 7, 127. Prime factorization of 1778 in exponential form is:

1778 = 2¹ × 7¹ × 127¹

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 1778

List of positive integer factors of 1778 that divides 1764 without a remainder.

1, 2, 7, 14, 127, 254, 889

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1764 and 1778. The biggest common factor number is the GCF number.
So the greatest common factor 1764 and 1778 is 14.

Also check out the Least Common Multiple of 1764 and 1778