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To sieve out every prime up to 50 you cross off the multiples of 2, then of 3, then of 5, then of 7 — and then you stop. Why is there no need to cross off the multiples of 11?

Class 6Playing with NumbersPlaying with Numbers
  • ABecause 11 is prime, so all its multiples are prime too.
  • BBecause is already past 50, so every composite up to 50 has a smaller prime factor and is gone already.
  • CBecause every multiple of 11 is also a multiple of 2.
  • DBecause 11 is bigger than half of 50.

Step-by-Step Solution

22, 33 and 44 were removed with the multiples of 2 and 3; the first multiple of 11 that nothing else has caught is , which is beyond 50. The trap is the first option — multiples of a prime are composite, not prime .
Answer: B) Because is already past 50, so every composite up to 50 has a smaller prime factor and is gone already.

Key idea: Multiples are unlimited

The multiples of 7 are 7, 14, 21, 28, 35, … — you get them by multiplying 7 by 1, 2, 3, 4, 5, …. Multiples never run out. Every number is a multiple of itself (and of 1). 0 is a multiple of every number, but we usually exclude it when listing multiples for practical work.

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