What is the Greatest Common Factor of 27680 and 27690?

Greatest common factor (GCF) of 27680 and 27690 is 10.

GCF(27680,27690) = 10

We will now calculate the prime factors of 27680 and 27690, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27680 and 27690.

How to find the GCF of 27680 and 27690?

We will first find the prime factorization of 27680 and 27690. After we will calculate the factors of 27680 and 27690 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 27690

Prime factors of 27690 are 2, 3, 5, 13, 71. Prime factorization of 27690 in exponential form is:

27690 = 2¹ × 3¹ × 5¹ × 13¹ × 71¹

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 27690

List of positive integer factors of 27690 that divides 27680 without a remainder.

1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 71, 78, 130, 142, 195, 213, 355, 390, 426, 710, 923, 1065, 1846, 2130, 2769, 4615, 5538, 9230, 13845

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27680 and 27690. The biggest common factor number is the GCF number.
So the greatest common factor 27680 and 27690 is 10.

Also check out the Least Common Multiple of 27680 and 27690