What is the Greatest Common Factor of 27678 and 27692?

Greatest common factor (GCF) of 27678 and 27692 is 14.

GCF(27678,27692) = 14

We will now calculate the prime factors of 27678 and 27692, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27678 and 27692.

How to find the GCF of 27678 and 27692?

We will first find the prime factorization of 27678 and 27692. After we will calculate the factors of 27678 and 27692 and find the biggest common factor number .

Step-1: Prime Factorization of 27678

Prime factors of 27678 are 2, 3, 7, 659. Prime factorization of 27678 in exponential form is:

27678 = 2¹ × 3¹ × 7¹ × 659¹

Step-2: Prime Factorization of 27692

Prime factors of 27692 are 2, 7, 23, 43. Prime factorization of 27692 in exponential form is:

27692 = 2² × 7¹ × 23¹ × 43¹

Step-3: Factors of 27678

List of positive integer factors of 27678 that divides 27678 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 659, 1318, 1977, 3954, 4613, 9226, 13839

Step-4: Factors of 27692

List of positive integer factors of 27692 that divides 27678 without a remainder.

1, 2, 4, 7, 14, 23, 28, 43, 46, 86, 92, 161, 172, 301, 322, 602, 644, 989, 1204, 1978, 3956, 6923, 13846

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27678 and 27692. The biggest common factor number is the GCF number.
So the greatest common factor 27678 and 27692 is 14.

Also check out the Least Common Multiple of 27678 and 27692