﻿ Multiples and dividers of a number. Exercises resolved.

# Multiples and dividers of a number. Exercises resolved.

I will now explain what the multiples and divisors of a number are. I’ll teach you how to get the multiples and divisors of a number.

It is very important to be very clear about this, as we are going to need it for many mathematical operations, such as fractions.

We’re starting!

## What are the multiples of a number?

When you multiply a number by any other natural number, the result is a multiple of the first number.

For example, if I multiply it by another number to 3, such as 2, the result is 6: Therefore, 6 is a multiple of 3.

Therefore, to obtain the multiples of a number, you only have to multiply that number by the natural numbers you want. For example, we are going to get four multiples of 5: We multiply the 5 by four different numbers and we have them. 10, 15, 20 and 25 are multiples of 5.

But how do you know if one number is a multiple of another?

Now let’s look at it in reverse. We have a number and they ask us if it’s a multiple of another one.

For that we have to divide those two numbers. If the division is exact, it will be a multiple.

For example, is 8 a multiple of 3?

Well, if we divide 8 by 3, the result isn’t accurate: Therefore, 8 is not a multiple of 3.

And 4 is a multiple of 8? The division is exact, so 8 is a multiple of 4.

In fact, if we multiply 4 by 2, as we saw at the beginning, we see that 8 is effectively a multiple of 4: Don’t worry if you’re having trouble understanding it now. Later on, we’ll take a lesson on how to explain it in detail and you’ll master it perfectly.

Now let’s go to the divisors. You will see that if you have understood what multiples are, you will understand the dividers very quickly.

## What are number dividers?

The divisors of a number are those that when dividing that number, the result is accurate.

For example, if 10 is divided by 2, the result is 5 (it is exact): The 2 is a divisor of 10, because dividing it gives an exact result.

And how do you know if a number is divisive from another?

Well, the only way is to do the splitting. If you look, it’s the same as when we were looking for the multiple of a number, when we asked if 8 is a multiple of 4: 8 is a multiple of 4, but 4 is a divisor of 8.

Similarly, in the above example, 10 is a multiple of 2

The multiples and dividers are related, so that:

• If a first number is a multiple of a second number, then the second number will be the divisor of the first number

What a mess, huh? Don’t worry about it. At the end of the course this will not be a problem for you.

And how do I know all the divisors of a number?

Knowing this doesn’t make much sense. Still, I’ll tell you how when you master warp decay.

What makes sense is knowing when one number can be divided by another without the need for division. This is very useful when we have large numbers and we will see it in detail later on.

Finally, and to make it clearer to you how to differentiate between multiples and divisors:

• The multiples of a number:
• They are always greater than that number
• They are infinite, because we can multiply that number by other infinite natural numbers
• The divisors of a number.
• They are always less than that number
• They are not infinite. Not all numbers can be divided by any number and the division must be exact

Now, I’ll let you practice with these exercises.

## Exercises solved on multiples and divisors

1 – Tell me 5 multiples of 6

2 – 10 is a multiple of 2? 10 is a multiple of 4? 10 is a multiple of 5?

3 – How do we know if a number is a divisor of another?

4 – Is 3 a divisor of 12? Is 10 a divisor of 6?

### Solutions

1 –

6 x 2= 12

6 x 3 = 18

6 x 4 = 24

6 x 5 = 30

6 x 6 = 36

10, 18, 24, 30 and 36 are multiples of 6

(In turn, 6 is a divisor of 12, 18, 24, 30 and 36, are you getting it?)

2 –

10:2 = 5 –> 10 is a multiple of 2 because the division gives accurate

10 is not a multiple of 4 because the division is not exact

10 = 2 is a multiple of 5 because the division is exact

(2 and 5 are divisors of 10)

3 – Because in making the division, the result is accurate

4 –

12:3 = 4 –> 3 is divisor of 12. The division is exact

10 cannot be divisor of 6 because on the one hand, it is greater than 6 and the divisors are smaller. On the other hand, the division, if we were to make it, is not exact either.