Rule of multiples of 6

The rule for multiples of 6 is as follows: If we divide a number by 6 the result is 0, then it is because it is a multiple of 6.In this new lesson from a Teacher we will see the rule of multiples of 6. We will start by understanding what a multiple is, to then see the rule of multiples of 6 and ending with some examples. It is a lesson typical of the subject of mathematics and is studied during primary school. Here we leave you a simple lesson with solved exercises for you to practice at home. Let's start!

Index

1. What are the multiples of a number?
2. How to know when a number is a multiple of 6? Ruler
3. Examples of multiples of 6
4. Exercises with multiples of 6
5. Solution to exercises with multiples of 6

The multiples of a number They are all those possible results that occur from multiplying that same number by all the natural numbers. This means that the multiples of a number they are infinite, except of course, zero.

When a number is part of another a certain number of times we can say that it is a multiple of that number.

examples

• Is 12 a multiple of 6? Yes, because 12 is twice the number 6 since 6 x 2 = 12
• Is 36 a multiple of 6? Yes, because 36 is six times the number 6 since 6 x 6 = 36

Here's the multiples of 6 rule! Multiples of 6 are multiples of 2 and 3 at the same time. That is, for a number to be a multiple of 6, it must be a multiple of 2 and 3.

The multiples of 2 are all numbers that end with an even number, while the multiples of 3 must contain 3 a certain number of times or if the digits that make up the number are divisible by 3.

Another way to know if a number is a multiple of another is through divisibility, that is, if a number is divisible by another, then it will be a multiple of this number.

Remember that a number is divisible by another if the result is an integer, or if its remainder is zero.

If we divide a number by 6 and its remainder is zero, or in other words its result is an integer, then that number is multiple of 6.

let's see some examples of multiples of 6 to finish understanding how to use the rule.

Is the number 216 a multiple of 6?

First we can see that the number ends in six, therefore it is an even number, then it is a multiple of 2 and we already have one point of our rule fulfilled. We add the figures 2 + 1 + 6 and we obtain 9, which is a multiple of 3, therefore we already have the second point of the rule fulfilled. So we can say that 216 is a multiple of 6.

Let's check by doing the division:

216 / 6 = 36

Is the number 108 a multiple of 6?

• is a multiple of 2 by ending with an even number
• is a multiple of 3 because 1 + 0 + 8 equals 9

So 108 is a multiple of 6. Let's check 108 / 6 = 18

Is the number 171 a multiple of 6?

The number 171 ends with an odd number, not with an even number, therefore the first rule of multiples of 6 is not fulfilled and therefore, we can say that 171 is NOT a multiple of 6.

Is the number 136 a multiple of 6?

• is a multiple of 2 because it ends with an even number.

• but it is NOT a multiple of 3 because the sum of its digits 1 + 3 + 6 is equal to 10, which is not a multiple of 3

Therefore, since the second rule is not fulfilled, then we can ensure that the number 136 is NOT a multiple of 6.

we leave you some exercises so you can apply what we learned in a Teacher. Once finished, you will see the solutions below.

Are the following numbers multiples of 6?

• 156
• 143
• 366
• 444
• 82
• 492
• 271
• 138

We provide you with the results along with the explanation of each of the exercises raised above.

• 156 is a multiple of 6 because it ends with an even number and the sum of its digits 1 + 5 + 6 is equal to 12, which is a multiple of 3. And 156 / 6 = 26
• 143 is NOT a multiple of 6 because its last number is NOT even, so it does not satisfy the first rule.
• 366 is a multiple of 6 because it ends with an even number and the sum of its digits 3 + 6 + 6 is equal to 15, which is a multiple of 3. And 366 / 6 = 61
• 444 is a multiple of 6 because it ends with an even number and the sum of its digits 4 + 4 + 4 is equal to 12, which is a multiple of 3. And 444 / 6 = 74
• 82 is NOT a multiple of 6 because its last digit is even, but the sum of its digits 8 + 2 is equal to 10, which is not a multiple of 3, so it does not meet the second rule.
• 492 is a multiple of 6 because it ends with an even number and the sum of its digits 4 + 9 + 2 is equal to 15, which is a multiple of 3. And 492 / 6 = 82
• 271 is NOT a multiple of 6 because its last digit is NOT even, so it does not satisfy the first rule.
• 138 is a multiple of 6 because it ends with an even number and the sum of its digits 1 + 3 + 8 is equal to 12, which is a multiple of 3. And 138 / 6 = 23

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