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Hint |
4) If the pattern below were continued, what number would be directly below 100?
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The numbers are an arithmetic sequence.
- Each row contains 2 more numbers than the previous row (1, 3, 5, 7 ...)
- The rows contain sequential numbers that are reversed in order from the previous row.
- You must find out which row 100 appears in and in what position in the row.
- Notice that the highest number in each row (1,4,9,16) are the squares of the row numbers (1,2,3,4).
- This means that 100 appears in the
N = ____th row.
- Also, notice that 100 is a square, itself.
- So the next number under the 100 is _____
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5) How many numbers between 100 and 1,000 have exactly 3 factors?
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- All numbers have 2 factors: 1 and the number itself.
Prime numbers have these factors only.
- The only numbers that have exactly 1 more factor are squares. For example the factors of 25 are 1, 5 and 25. But only numbers whose square roots are primes, otherwise there will be additional factors.
- Numbers that have prime square roots:
- There are ____ numbers between 100 and 1000 that have 3 factors.
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