What is the Greatest Common Factor of 27680 and 27688?

Greatest common factor (GCF) of 27680 and 27688 is 8.

GCF(27680,27688) = 8

We will now calculate the prime factors of 27680 and 27688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27680 and 27688.

How to find the GCF of 27680 and 27688?

We will first find the prime factorization of 27680 and 27688. After we will calculate the factors of 27680 and 27688 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 27688

Prime factors of 27688 are 2, 3461. Prime factorization of 27688 in exponential form is:

27688 = 2³ × 3461¹

Step-3: Factors of 27680

List of positive integer factors of 27680 that divides 27680 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

Step-4: Factors of 27688

List of positive integer factors of 27688 that divides 27680 without a remainder.

1, 2, 4, 8, 3461, 6922, 13844

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27680 and 27688. The biggest common factor number is the GCF number.
So the greatest common factor 27680 and 27688 is 8.

Also check out the Least Common Multiple of 27680 and 27688