What is the Greatest Common Factor of 27738 and 27746?

Greatest common factor (GCF) of 27738 and 27746 is 2.

GCF(27738,27746) = 2

We will now calculate the prime factors of 27738 and 27746, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27738 and 27746.

How to find the GCF of 27738 and 27746?

We will first find the prime factorization of 27738 and 27746. After we will calculate the factors of 27738 and 27746 and find the biggest common factor number .

Step-1: Prime Factorization of 27738

Prime factors of 27738 are 2, 3, 23, 67. Prime factorization of 27738 in exponential form is:

27738 = 2¹ × 3² × 23¹ × 67¹

Step-2: Prime Factorization of 27746

Prime factors of 27746 are 2, 13873. Prime factorization of 27746 in exponential form is:

27746 = 2¹ × 13873¹

Step-3: Factors of 27738

List of positive integer factors of 27738 that divides 27738 without a remainder.

1, 2, 3, 6, 9, 18, 23, 46, 67, 69, 134, 138, 201, 207, 402, 414, 603, 1206, 1541, 3082, 4623, 9246, 13869

Step-4: Factors of 27746

List of positive integer factors of 27746 that divides 27738 without a remainder.

1, 2, 13873

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27738 and 27746. The biggest common factor number is the GCF number.
So the greatest common factor 27738 and 27746 is 2.

Also check out the Least Common Multiple of 27738 and 27746