Bonus: what is a number made of?

Hello, and welcome to Myriora Maths! Here's a question for you. What is thirty-six times twenty-five? You could work it out the long way. But there's a way to see the answer, if you know what these numbers are made of.

Imagine that every number is a gem. Some gems are pure. Two, three, five and seven can't be split into smaller gems. In maths, we call them prime numbers. Other gems are made from pure gems. Six is made from a two and a three. Eighty-four is made from two, two, three and seven. Multiplying hides the pure gems inside. Factorisation finds them again. It simply asks: what is this number made of?

Here's why that's a good question. Twelve can split as two times six. Or it can split as three times four. Keep splitting, and both paths end with the same pure gems: two, two and three. Every whole number above one has just one set of pure gems. It's like the number's fingerprint.

So what can you do with them? First, you can move them around. Thirty-six is two, two, three and three. Twenty-five is five and five. When you multiply, the order doesn't matter, so we can pair them up. A two and a five make ten. Do it again, and ten times ten is a hundred. The two threes left over make nine. So the answer is nine hundred.

Second, you can see what divides a number, without dividing. Eighty-four has the gems two, two, three and seven. Does six go into eighty-four? Six needs a two and a three. They're both there, so yes. Does eight go into eighty-four? Eight needs three twos, but there are only two. So no. A factor is a number whose gems are all inside.

Third, dividing is just taking gems out. Here's eighty-four divided by fourteen. Fourteen is a two and a seven. Take them out. A two and a three are left, and that makes six. So eighty-four divided by fourteen is six.

Let's try one together. What is forty-five times eighteen? Here's a tip: find a pair that makes ten. Say it out loud!

Forty-five is three, three and five. Eighteen is two, three and three. The two and the five make ten. The four threes make eighty-one. So the answer is eight hundred and ten.

Here's a common mistake. Eighty-four divides by two, and it divides by four. So you might say it divides by eight. But the answer is no. The four already uses both of the twos, and eight needs a third.

Your turn! Sixty is two, two, three and five. Which number goes into sixty? Pick the right card. You've got ten seconds, or pause the video. Go!

Time's up! The answer is twelve! Twelve needs two, two and three, and they're all there. Take them out, and a five is left, so sixty divided by twelve is five.

Quick review. Factorisation asks what a number is made of. Every whole number above one has one set of pure gems. Move them around to make easy pairs. Compare gems to see what divides. And take gems out to divide.

These gems come from a game we made, called Factor Gems. In its Gem Workshop, you can merge gems and split them. When you match gems, they're divided, just like taking a gem out. Ask a grown-up if you'd like to try it. See you next time!