Question:medium

What is the sum of the factors of 27000?

Updated On: Jun 30, 2026
  • 11700
  • 23400
  • 46800
  • 70200
  • 93600
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The Correct Option is

Solution and Explanation

The correct answer is option (E):
93600

To find the sum of the factors of 27000, we first need to prime factorize 27000. We can do this as follows:

27000 = 27 * 1000
27000 = 3 * 9 * 10 * 100
27000 = 3 * 3 * 3 * 2 * 5 * 2 * 5 * 2 * 5
27000 = 2^3 * 3^3 * 5^3

Now, to find the sum of the factors, we use the following formula, which is derived from the expansion of (1 + p + p^2 + ... + p^a)(1 + q + q^2 + ... + q^b)(1 + r + r^2 + ... + r^c), where the prime factorization is p^a * q^b * r^c:

Sum of factors = (1 + 2 + 2^2 + 2^3) * (1 + 3 + 3^2 + 3^3) * (1 + 5 + 5^2 + 5^3)

Let's calculate each part:

(1 + 2 + 2^2 + 2^3) = (1 + 2 + 4 + 8) = 15
(1 + 3 + 3^2 + 3^3) = (1 + 3 + 9 + 27) = 40
(1 + 5 + 5^2 + 5^3) = (1 + 5 + 25 + 125) = 156

Now, multiply these sums together:

15 * 40 * 156 = 93600

Therefore, the sum of the factors of 27000 is 93600.
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