What is the Greatest Common Factor of 27665 and 27680?

Greatest common factor (GCF) of 27665 and 27680 is 5.

GCF(27665,27680) = 5

We will now calculate the prime factors of 27665 and 27680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27665 and 27680.

How to find the GCF of 27665 and 27680?

We will first find the prime factorization of 27665 and 27680. After we will calculate the factors of 27665 and 27680 and find the biggest common factor number .

Step-1: Prime Factorization of 27665

Prime factors of 27665 are 5, 11, 503. Prime factorization of 27665 in exponential form is:

27665 = 5¹ × 11¹ × 503¹

Step-2: Prime Factorization of 27680

Prime factors of 27680 are 2, 5, 173. Prime factorization of 27680 in exponential form is:

27680 = 2⁵ × 5¹ × 173¹

Step-3: Factors of 27665

List of positive integer factors of 27665 that divides 27665 without a remainder.

1, 5, 11, 55, 503, 2515, 5533

Step-4: Factors of 27680

List of positive integer factors of 27680 that divides 27665 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160, 173, 346, 692, 865, 1384, 1730, 2768, 3460, 5536, 6920, 13840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27665 and 27680. The biggest common factor number is the GCF number.
So the greatest common factor 27665 and 27680 is 5.

Also check out the Least Common Multiple of 27665 and 27680