January 2023 Brain Puzzler Solution

Q: Without a calculator or the Internet, find the prime factors of 2023.

A: Try prime numbers.
First: 2 the number is not even so 2 is not a factor.
For 3, we have to check the sum of the digits which total to 7 which is not divisible by 3, therefore 2023 is not divisible by 3.
For 5, the number doesn’t end in 5 or 0 so not divisible by 5.
For 7, think of a number close that is divisible by 7 — 2100 is 300 x 7.
2023 is 77 less than 2100. Since 77 is also divisible by 7, 2023 is a multiple of 7. It is 300 x 7 – 11 x 7 which is 289 x 7.
289 happens to be a perfect square as it is 17 x 17.

Since 17 is prime, it cannot be factored any further.

So the prime factors of 2023 are: 7 x 17 x 17.


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