What is the Greatest Common Factor of 1774 and 1780?

Greatest common factor (GCF) of 1774 and 1780 is 2.

GCF(1774,1780) = 2

We will now calculate the prime factors of 1774 and 1780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1774 and 1780.

How to find the GCF of 1774 and 1780?

We will first find the prime factorization of 1774 and 1780. After we will calculate the factors of 1774 and 1780 and find the biggest common factor number .

Step-1: Prime Factorization of 1774

Prime factors of 1774 are 2, 887. Prime factorization of 1774 in exponential form is:

1774 = 2¹ × 887¹

Step-2: Prime Factorization of 1780

Prime factors of 1780 are 2, 5, 89. Prime factorization of 1780 in exponential form is:

1780 = 2² × 5¹ × 89¹

Step-3: Factors of 1774

List of positive integer factors of 1774 that divides 1774 without a remainder.

1, 2, 887

Step-4: Factors of 1780

List of positive integer factors of 1780 that divides 1774 without a remainder.

1, 2, 4, 5, 10, 20, 89, 178, 356, 445, 890

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1774 and 1780. The biggest common factor number is the GCF number.
So the greatest common factor 1774 and 1780 is 2.

Also check out the Least Common Multiple of 1774 and 1780