What is the Greatest Common Factor of 17774 and 17780?

Greatest common factor (GCF) of 17774 and 17780 is 2.

GCF(17774,17780) = 2

We will now calculate the prime factors of 17774 and 17780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17774 and 17780.

How to find the GCF of 17774 and 17780?

We will first find the prime factorization of 17774 and 17780. After we will calculate the factors of 17774 and 17780 and find the biggest common factor number .

Step-1: Prime Factorization of 17774

Prime factors of 17774 are 2, 8887. Prime factorization of 17774 in exponential form is:

17774 = 2¹ × 8887¹

Step-2: Prime Factorization of 17780

Prime factors of 17780 are 2, 5, 7, 127. Prime factorization of 17780 in exponential form is:

17780 = 2² × 5¹ × 7¹ × 127¹

Step-3: Factors of 17774

List of positive integer factors of 17774 that divides 17774 without a remainder.

1, 2, 8887

Step-4: Factors of 17780

List of positive integer factors of 17780 that divides 17774 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 127, 140, 254, 508, 635, 889, 1270, 1778, 2540, 3556, 4445, 8890

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17774 and 17780. The biggest common factor number is the GCF number.
So the greatest common factor 17774 and 17780 is 2.

Also check out the Least Common Multiple of 17774 and 17780