Isha checks whether 49 is prime. She finds 49 is not divisible by 2, not by 3, not by 5 — and…
Isha checks whether 49 is prime. She finds 49 is not divisible by 2, not by 3, not by 5 — and concludes 49 is prime. Her brother says she skipped a number she needed to check. Who is right?
Who do you think is right? Pick one.
The answer: Her brother is right, she did not check 7 — and 49 = 7 x 7
Why
Isha checked a reasonable-looking set of small numbers, but she stopped one short. To be sure a number is prime, you have to try dividing it by every prime up to its square root — because if a number splits into two factors, at least one of them must be no bigger than the square root. The square root of 49 is 7, so 7 is exactly the number she needed to test, and she went 2, 3, 5 and skipped straight past it. Test it: 49 divided by 7 is exactly 7, no remainder — so 49 = 7 x 7, which means 49 is composite, not prime. Her brother is right: she missed 7, and 49 = 7 x 7 — checking only 2, 3, and 5 is not enough; you must check every prime up to the square root.
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