A "Pure Factor" of a natural number "n" is that factor of n which has

Question

A "Pure Factor" of a natural number "n" is that factor of n which has only one prime factor. S(n) is the sum of all the pure factors of of n, what is the value of S(3000)?

(A) 9
(B) 170
(C) 171
(D) 172
(E) 173

chetan2u · Answer

Not the correct way to post the question.

Otherwise the first step would be to prime factorise the number 
 3000=3*2^3*5^3 
If the prime factor is 2: 2, 2^2 or 4 and 2^3 or 8
If the prime factor is 3: 3
If the prime factor is 5: 5, 5^2 or 25 and 5^3 or 125

Sum = 2+4+8+3+5+25+125=172

onlymalapink · Answer

I can see what is done I dont understand the question please help explain what it meant by the factors

Bunuel · Answer

A factor is a positive divisor, while a "Pure Factor" is defined as a factor that has only one prime factor.

For example, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The pure factors of 36 are only those that contain a single prime factor: 2, 3, 4, and 9. While, for instance, 12 = 2^2 * 3 would not be considered a pure factor because it has two primes, 2 and 3.

The question asks for the sum of the pure factors of 3,000.

Factorizing: 3,000 = 2^3 * 3 * 5^3

The total number of factors is (3 + 1)(1 + 1)(3 + 1) = 32. However, only the factors that consist of a single prime are pure factors. These are:

2, 2^2, 2^3, 3, 5, 5^2, and 5^3

Summing them: 2 + 2^2 + 2^3 + 3 + 5 + 5^2 + 5^3 = 172

Answer: D.

MagnusSamIBA · Answer

As we want to solve for S(3000), we first need to find the prime factorization of 3000, which is 3000 = 2^3 * 3 * 5^3.

Next, we identify the "pure factors" of 3000, which are factors that consist of only one prime factor. For the prime factor 2, the pure factors are 2, 4, and 8. For 3, the pure factor is just 3. For 5, the pure factors are 5, 25, and 125.

Now, we sum these pure factors: 2 + 4 + 8 + 3 + 5 + 25 + 125 = 172.

Thus, the value of S(3000) is 172.

Ans- D

A "Pure Factor" of a natural number "n" is that factor of n which has

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A "Pure Factor" of a natural number "n" is that factor of n which has

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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