Trinny says, “When you multiply two even numbers together, the answer is always an odd number.” Part a) Write down an example that disproves Trinny’s statement. Zack says, “I can multiply two factors of 81 together to give an even number.” Part b) Explain why Zack is mistaken.
So when dealing with part a, the first thing we need to look at is an even number. So what is an even number? Well, an even number is a number that is divisible by two. And when we say this, we mean it is divisible exactly by two with no remainder.
What Trinny says that when you multiply two even numbers together, the answer is always an odd number. But we know that if you multiply an even number by an even number, the answer is even. So therefore, what we need to do is actually write down an example of this to disprove Trinny’s statement.
To do this, what I’m gonna do is actually pick the first two even numbers, two and four, and multiply them together. And when I do this, I get an answer of eight and eight is an even number.
So therefore, what I’ve done is actually written down an example that disproves Trinny’s statement because I’ve shown that two multiplied by four equals eight. Eight is an even number. So it’s shown that even multiplied by an even gives an answer that is even.
So now, what we’re gonna do is move on to part b. So what we want to do with part b is actually multiply two factors of 81 together. And a factor is actually a number that multiplies by another number to make a result we’re looking for, so in this case 81.
So therefore, the first thing we want to so is actually find the factors of 81. And to do this, we’re actually gonna list them in pairs, the first of which are one and 81. And that’s because one multiplied by 81 gives us 81. Then, we’ve got three and 27 cause three multiplied by 27 is 81. Two wouldn’t work because 81 isn’t an even number. So it cannot be divided by two. And then, our final factor will be nine and that’s because nine multiplied by nine gives us 81.
We could have tried four, but that wouldn’t have gone in because it’s an even number; five that wouldn’t have gone into 81 because 81 doesn’t end in a zero or five. And we can carry on trying six, seven, and eight and none of these would have actually gone into 81.
We don’t have to consider anything greater than nine and that’s because we had nine multiplied by nine, which means that if we went any higher than nine, our factor would have to be less than nine and we’ve already checked those ones through. So therefore, we can say the factors of 81 are one, three, nine, 27, and 81.
So therefore, we can actually say that when Zack says, “I can multiply two factors of 81 together to give an even number,” he is mistaken because all the factors of 81 are odd. And we know that an odd multiplied by an odd gives us a result that is an odd.