What is the Greatest Common Factor of 27748 and 27762?

Greatest common factor (GCF) of 27748 and 27762 is 14.

GCF(27748,27762) = 14

We will now calculate the prime factors of 27748 and 27762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27748 and 27762.

How to find the GCF of 27748 and 27762?

We will first find the prime factorization of 27748 and 27762. After we will calculate the factors of 27748 and 27762 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 27762

Prime factors of 27762 are 2, 3, 7, 661. Prime factorization of 27762 in exponential form is:

27762 = 2¹ × 3¹ × 7¹ × 661¹

Step-3: Factors of 27748

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

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

Step-4: Factors of 27762

List of positive integer factors of 27762 that divides 27748 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 661, 1322, 1983, 3966, 4627, 9254, 13881

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27748 and 27762. The biggest common factor number is the GCF number.
So the greatest common factor 27748 and 27762 is 14.

Also check out the Least Common Multiple of 27748 and 27762