What is the Greatest Common Factor of 17774 and 17782?

Greatest common factor (GCF) of 17774 and 17782 is 2.

GCF(17774,17782) = 2

We will now calculate the prime factors of 17774 and 17782, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17774 and 17782.

How to find the GCF of 17774 and 17782?

We will first find the prime factorization of 17774 and 17782. After we will calculate the factors of 17774 and 17782 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 17782

Prime factors of 17782 are 2, 17, 523. Prime factorization of 17782 in exponential form is:

17782 = 2¹ × 17¹ × 523¹

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 17782

List of positive integer factors of 17782 that divides 17774 without a remainder.

1, 2, 17, 34, 523, 1046, 8891

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17774 and 17782. The biggest common factor number is the GCF number.
So the greatest common factor 17774 and 17782 is 2.

Also check out the Least Common Multiple of 17774 and 17782