What is the Greatest Common Factor of 27734 and 27742?

Greatest common factor (GCF) of 27734 and 27742 is 2.

GCF(27734,27742) = 2

We will now calculate the prime factors of 27734 and 27742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27734 and 27742.

How to find the GCF of 27734 and 27742?

We will first find the prime factorization of 27734 and 27742. After we will calculate the factors of 27734 and 27742 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 27742

Prime factors of 27742 are 2, 11, 13, 97. Prime factorization of 27742 in exponential form is:

27742 = 2¹ × 11¹ × 13¹ × 97¹

Step-3: Factors of 27734

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

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

Step-4: Factors of 27742

List of positive integer factors of 27742 that divides 27734 without a remainder.

1, 2, 11, 13, 22, 26, 97, 143, 194, 286, 1067, 1261, 2134, 2522, 13871

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27734 and 27742. The biggest common factor number is the GCF number.
So the greatest common factor 27734 and 27742 is 2.

Also check out the Least Common Multiple of 27734 and 27742