# Polynomials

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## Factors

What is the sum of all numbers less than 200 that are either prime or have more than 3 factors?
1. 19900
2. 19533
3. 19522
4. 19534

Choice C. 19522

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## Detailed Solution

Only number that has exactly one factor is 1
Which numbers have exactly 2 factors?
This would be the list of prime numbers
Which numbers have more than 2 factors?
All composite numbers have more than 2 factors.
Which numbers have exactly 3 factors?
Squares of prime numbers have exactly 3 factors.
Sum of all numbers either prime or have more than 3 factors can be obtained by
Sum of all natural numbers less than 200 - Sum of numbers with 1 or 3 factors.
Numbers with 1 or 3 factors = 1, 4, 9, 25, 49, 121, 169
Sum of remaining numbers = (1 + 2 + 3 + 4 + 5 …..199)
– (1 + 4 + 9 + 25 + 49 + 121 + 169)
= 19900 - 378 = 19522

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