What is the Greatest Common Factor of 27824 and 27830?

Greatest common factor (GCF) of 27824 and 27830 is 2.

GCF(27824,27830) = 2

We will now calculate the prime factors of 27824 and 27830, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27824 and 27830.

How to find the GCF of 27824 and 27830?

We will first find the prime factorization of 27824 and 27830. After we will calculate the factors of 27824 and 27830 and find the biggest common factor number .

Step-1: Prime Factorization of 27824

Prime factors of 27824 are 2, 37, 47. Prime factorization of 27824 in exponential form is:

27824 = 2⁴ × 37¹ × 47¹

Step-2: Prime Factorization of 27830

Prime factors of 27830 are 2, 5, 11, 23. Prime factorization of 27830 in exponential form is:

27830 = 2¹ × 5¹ × 11² × 23¹

Step-3: Factors of 27824

List of positive integer factors of 27824 that divides 27824 without a remainder.

1, 2, 4, 8, 16, 37, 47, 74, 94, 148, 188, 296, 376, 592, 752, 1739, 3478, 6956, 13912

Step-4: Factors of 27830

List of positive integer factors of 27830 that divides 27824 without a remainder.

1, 2, 5, 10, 11, 22, 23, 46, 55, 110, 115, 121, 230, 242, 253, 506, 605, 1210, 1265, 2530, 2783, 5566, 13915

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27824 and 27830. The biggest common factor number is the GCF number.
So the greatest common factor 27824 and 27830 is 2.

Also check out the Least Common Multiple of 27824 and 27830