Victoria says, “When you halve a whole number ending in six, you always get a number ending in three.” Give an example to show that Victoria is incorrect.
To show that she’s incorrect, we just need to find one situation for which this is false. Let’s choose some numbers then that end in six. The first number that we can choose is six. Six divided by two is three, so for this number, she’s correct. The next number that ends in a six is 16. 16 divided by two is eight. Eight does not end in the number three. So this is an example we can use to show that Victoria is incorrect.
Jake says, “Since three, 13, and 23 are all prime numbers, all whole numbers that end in three are prime numbers.” Is Jake correct? You must justify your answer.
Once again, let’s check whether he’s correct by trying a few numbers. If we can’t find any numbers for which he is incorrect, then we’ll need to use some logic to prove that he is correct. Remember, it’s not enough just to say yes or no. We do need to follow this process to get all of the marks.
Remember, a prime number is a number which has exactly two factors, one and itself. We’ve seen that three, 13, and 23 are all prime numbers. Three is equivalent to one multiplied by three. There are no other factors. Similarly, 13 is one multiplied by 13, and 23 is one multiplied by 23.
So let’s find the next number that ends in a three. It’s 33. 33 can indeed be written as one multiplied by 33, but it can also be written as three multiplied by 11. Since it has four factors, the number 33 cannot be a prime number. Jake is incorrect. 33 is not a prime number. And that is our full justification for this answer.