What is the Greatest Common Factor of 7774 and 7782?

Greatest common factor (GCF) of 7774 and 7782 is 2.

GCF(7774,7782) = 2

We will now calculate the prime factors of 7774 and 7782, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7774 and 7782.

How to find the GCF of 7774 and 7782?

We will first find the prime factorization of 7774 and 7782. After we will calculate the factors of 7774 and 7782 and find the biggest common factor number .

Step-1: Prime Factorization of 7774

Prime factors of 7774 are 2, 13, 23. Prime factorization of 7774 in exponential form is:

7774 = 2¹ × 13² × 23¹

Step-2: Prime Factorization of 7782

Prime factors of 7782 are 2, 3, 1297. Prime factorization of 7782 in exponential form is:

7782 = 2¹ × 3¹ × 1297¹

Step-3: Factors of 7774

List of positive integer factors of 7774 that divides 7774 without a remainder.

1, 2, 13, 23, 26, 46, 169, 299, 338, 598, 3887

Step-4: Factors of 7782

List of positive integer factors of 7782 that divides 7774 without a remainder.

1, 2, 3, 6, 1297, 2594, 3891

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7774 and 7782. The biggest common factor number is the GCF number.
So the greatest common factor 7774 and 7782 is 2.

Also check out the Least Common Multiple of 7774 and 7782