What is the Greatest Common Factor of 27680 and 27698?

Greatest common factor (GCF) of 27680 and 27698 is 2.

GCF(27680,27698) = 2

We will now calculate the prime factors of 27680 and 27698, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27680 and 27698.

How to find the GCF of 27680 and 27698?

We will first find the prime factorization of 27680 and 27698. After we will calculate the factors of 27680 and 27698 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 27698

Prime factors of 27698 are 2, 11, 1259. Prime factorization of 27698 in exponential form is:

27698 = 2¹ × 11¹ × 1259¹

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 27698

List of positive integer factors of 27698 that divides 27680 without a remainder.

1, 2, 11, 22, 1259, 2518, 13849

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27680 and 27698. The biggest common factor number is the GCF number.
So the greatest common factor 27680 and 27698 is 2.

Also check out the Least Common Multiple of 27680 and 27698