What is the Greatest Common Factor of 27742 and 27754?

Greatest common factor (GCF) of 27742 and 27754 is 2.

GCF(27742,27754) = 2

We will now calculate the prime factors of 27742 and 27754, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27742 and 27754.

How to find the GCF of 27742 and 27754?

We will first find the prime factorization of 27742 and 27754. After we will calculate the factors of 27742 and 27754 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 27754

Prime factors of 27754 are 2, 13877. Prime factorization of 27754 in exponential form is:

27754 = 2¹ × 13877¹

Step-3: Factors of 27742

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

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

Step-4: Factors of 27754

List of positive integer factors of 27754 that divides 27742 without a remainder.

1, 2, 13877

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27742 and 27754. The biggest common factor number is the GCF number.
So the greatest common factor 27742 and 27754 is 2.

Also check out the Least Common Multiple of 27742 and 27754