Investigate the Number 31: Is it a Prime?

Check if 31 is divisible by any prime numbers smaller than $\sqrt{31} \approx 5.6$. Test primes 2, 3, and 5. Since 31 ÷ 2 = 15.5, 31 ÷ 3 = 10.33..., and 31 ÷ 5 = 6.2, none divide evenly!

If 31 had a factor larger than $\sqrt{31}$, it would need a corresponding smaller factor to multiply together and equal 31. Since we already checked all smaller factors, we're done!

Look at the last digit only! If it's 0, 2, 4, 6, or 8, the number is divisible by 2. Since 31 ends in 1, it's not divisible by 2.

Check if the last two digits form a number divisible by 4. For 31, the last two digits are "31". Since 31 ÷ 4 = 7.75 (not a whole number), 31 isn't divisible by 4.

Any number divisible by 10 must end in 0. That's it! Since 31 ends in 1, it's definitely not divisible by 10.

Divisibility by 3: Add all digits. If the sum is divisible by 3, so is the original number. For 31: 3 + 1 = 4, and 4 ÷ 3 isn't whole, so 31 isn't divisible by 3!