High School

Let \( n = 2^s \times 39 \times 52 \times 197 \).

Which of the following are factors of \( n \)?

a) 13
b) 39
c) 52
d) 197

Answer :

Final answer:

All options given (a) 13, (b) 39, (c) 52, and (d) 197 are factors of the number n = 2^s x 39 x 52 x 197, hence they are all correct.

Explanation:

The question asks us to determine which of the given options are factors of the number n = 2s x 39 x 52 x 197. A factor is a number that divides into another number without leaving a remainder. To identify the factors of n, we should examine its prime factorization. In this problem, the numbers 39, 52, and 197 are already provided as factors, and 2s indicates that 2 is also a factor raised to some power s.

Breaking down the factors:

  • 39 can be factored into 3 and 13.
  • 52 can be factored into 4 (which is 22) and 13.
  • 197 is a prime number and cannot be factored further.

Given these factorizations, we can see that:

  1. 13 is a factor of both 39 and 52, so it is a factor of n.
  2. 39 is explicitly given as a factor of n.
  3. 52 is explicitly given as a factor of n.
  4. 197 is explicitly given as a factor of n.

Therefore, all options given (a) 13, (b) 39, (c) 52, and (d) 197 are correct and are factors of n.

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