What is the Greatest Common Factor of 27734 and 27748?

Greatest common factor (GCF) of 27734 and 27748 is 14.

GCF(27734,27748) = 14

We will now calculate the prime factors of 27734 and 27748, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27734 and 27748.

How to find the GCF of 27734 and 27748?

We will first find the prime factorization of 27734 and 27748. After we will calculate the factors of 27734 and 27748 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 27748

Prime factors of 27748 are 2, 7, 991. Prime factorization of 27748 in exponential form is:

27748 = 2² × 7¹ × 991¹

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 27748

List of positive integer factors of 27748 that divides 27734 without a remainder.

1, 2, 4, 7, 14, 28, 991, 1982, 3964, 6937, 13874

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27734 and 27748. The biggest common factor number is the GCF number.
So the greatest common factor 27734 and 27748 is 14.

Also check out the Least Common Multiple of 27734 and 27748