What is the Greatest Common Factor of 27714 and 27734?

Greatest common factor (GCF) of 27714 and 27734 is 2.

GCF(27714,27734) = 2

We will now calculate the prime factors of 27714 and 27734, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27714 and 27734.

How to find the GCF of 27714 and 27734?

We will first find the prime factorization of 27714 and 27734. After we will calculate the factors of 27714 and 27734 and find the biggest common factor number .

Step-1: Prime Factorization of 27714

Prime factors of 27714 are 2, 3, 31, 149. Prime factorization of 27714 in exponential form is:

27714 = 2¹ × 3¹ × 31¹ × 149¹

Step-2: Prime Factorization of 27734

Prime factors of 27734 are 2, 7, 283. Prime factorization of 27734 in exponential form is:

27734 = 2¹ × 7² × 283¹

Step-3: Factors of 27714

List of positive integer factors of 27714 that divides 27714 without a remainder.

1, 2, 3, 6, 31, 62, 93, 149, 186, 298, 447, 894, 4619, 9238, 13857

Step-4: Factors of 27734

List of positive integer factors of 27734 that divides 27714 without a remainder.

1, 2, 7, 14, 49, 98, 283, 566, 1981, 3962, 13867

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27714 and 27734. The biggest common factor number is the GCF number.
So the greatest common factor 27714 and 27734 is 2.

Also check out the Least Common Multiple of 27714 and 27734