# Multiples of 10

**Ten** is the first two-digit even number that comes after 9 and before 11. Having ten

fingers and ten toes may have probably led our early mathematicians to consider ten as the base value in our decimal number system.

For some, 10 is considered as the *end* of a *cycle* and *perfection*. Pythagoras and his

followers considered 10 to be the most sacred number of all.

This is because adding numbers from 1 to 4 will be equivalent to 10 – which for them signifies existence (1), creation (2), life (3), and the elements of earth, air, fire, and water.

10 is indeed an important number in our number system – and knowing more numbers that are connected to this number can also be of great help to our lives.

Are you ready to board another journey of finding multiples of 10? Say no more as we start our flight towards this exciting expedition!

## Multiples of 10 are 10, 20, 30, 40, 50, 60, 70 …

When an integer is multiplied by ten, the products are multiples of ten. A multiple of 10 is a sequence in which the difference between its consecutive numbers is 10.

Multiples of 10 can also mean that every time a number is divided by 10, it will always result to a zero remainder. We can acquire a positive multiple of 10 by simply multiplying 10 to any positive number.

Similarly, multiplying 10 to any negative integer yields a negative multiple of 10. Remember that fractions cannot be utilized to generate a multiple of 10 because a whole number is required.

## 10 as a factor and multiple

There is an **endless number** of multiples of ten. However, its factor will always be **finite**. There are only four exact factors of 10, which are 1, 2, 5, and 10. On the other hand, the multiples of 10 are 10, 20, 30, 40, 50… and so on.

Now, let’s take a look at this table.

Multiples of 2, 5, and 10 | Multiples of 2 that are not multiples of 10 | Multiples of 5 that are not multiples of 10 |
---|---|---|

All multiples of 10 are also multiples of 2 and 5, such as 10, 20, 30, 40, 50, etc. |
2, 4, 8, 14, 16, and so on are all multiples of two but not multiples of ten. |
Some of the multiples of 5 that are not multiples of 10 are 5, 15, 25, 35, 45… and so on. |

The table above shows that even though all multiples of 10 are also a multiple of 2 and 5, it does not mean that every multiple of 2 and 5 are also multiples of 10.

Now, let’s journey further in determining the multiples of 10.

## How to find the multiples of 10?

Multiples of 10 are as easy as counting 123s – and so as finding its n^{th} multiple. We can do this by using the two previously learned methods – **skip counting and ****multiplication!**

To find the consecutive multiples of 10 through skip counting, we will start with 10. Then, to find the next multiple, we will simply add 10.

Hence, 10 + 10 = 20.

Skip counting is also referred to

as repeated addition – which means, to get any multiple of 10, we will repeat adding 10 until we get to the n^{th} we want to get.

Now, since we now know that adding two 10s will result to 20, adding another 10 will give us the result of 30.

Now, let’s look try another method in finding multiples of 10.

Multiplication is the faster way we can solve to get any multiples of a number. When we say that a number can be expressed as 10*n*, we are certain that it is a multiple of 10.

For example, to find the 45^{th} multiple of 10, we will simply multiply 10 by 45. Hence, **10 x 45 = 450**. This is a more convenient way than adding 10 repeatedly for 45 times.

Now, let’s take a look at this table.

n^{th} Multiple | Skip Counting | Multiplication |
---|---|---|

1 |
10 |
10 x 1 = 10 |

2 |
10 + 10 = 20 |
10 x 2 = 20 |

3 |
10 + 10 + 10 = 30 |
10 x 3 = 30 |

4 |
10 + 10 + 10 + 10 = 40 |
10 x 4 = 40 |

5 |
10 + 10 + 10 + 10 + 10 = 50 |
10 x 5 = 50 |

Notice how the outcome of skip-counting and multiplication will always give the same result? This is due to the fact that both are methods in finding any multiples of 10.

However, for some, they see multiplication as a quicker method.

## Did you know that…

Multiplying any number by multiples of ten is much easier than conventional

multiplication? This can be done by simply copying the n^{th}multiple we are looking for and adding the trailing 0 at the end of the number!

Say, we are looking for the 9^{th} multiple of 10. Using this method, we simply copy 9, and add 0 after 9. Thus, we have 90!

Let’s try another one! Suppose we are looking for the 25^{th} multiple of 10. Using this technique, we have 25 – and adding 0 to it will result to 250!

It is very simple and remarkable, isn’t it?

## List of the First 30 multiples of 10

The table displays the first 30 positive multiples of 10 as well as how it is formed. We can readily see that multiplying any number by 10 produces various multiples of 10.

Product of 10 and a positive counting number | Multiples of 10 |
---|---|

10 x 1 | 10 |

10 x 2 | 20 |

10 x 3 | 30 |

10 x 4 | 40 |

10 x 5 | 50 |

10 x 6 | 60 |

10 x 7 | 70 |

10 x 8 | 80 |

10 x 9 | 90 |

10 x 10 | 100 |

10 x 11 | 110 |

10 x 12 | 120 |

10 x 13 | 130 |

10 x 14 | 140 |

10 x 15 | 150 |

10 x 16 | 160 |

10 x 17 | 170 |

10 x 18 | 180 |

10 x 19 | 190 |

10 x 20 | 200 |

10 x 21 | 210 |

10 x 22 | 220 |

10 x 23 | 230 |

10 x 24 | 240 |

10 x 25 | 250 |

10 x 26 | 260 |

10 x 27 | 270 |

10 x 28 | 280 |

10 x 29 | 290 |

10 x 30 | 300 |

Did you notice something?

If we get any multiples of 10, we will always have a result that ends with 0! This observation will help us easily determine that a number is a multiple of 10.

## Solving problems involving multiples of 10

Now, let’s try solving real-life problems that involve multiples of 10.

### Problem #1

Sandara decided to count all the ten-dollar bills she had. She found out that she had 20 ten-dollar bills in her wallet, 2 ten-dollar bills in her pocket, and 5 ten-dollar bills she found in her room. How much money does Sandara have?

To solve this problem, we need to find the total number of ten-dollar bills Sandara has. We can do this by adding all the ten-dollar bills she found in her wallet, pocket, and room. Thus, **20 + 2 + 5 = 27**.

Then, to find the total money Sandara has, we are simply going to multiply 27 by ten dollars.

Hence, **27 x $10 = $270**.

Therefore, Sandara’s total money is **$270**.

Now, let’s try to work on another problem.

### Problem #2

Rexford joined a team building in their school fair. On one of the tasks, they were given a clue that they needed to answer to proceed to the next station. The clue says:

Determine the number that is being described.

- It should be a common multiple of 10 and 7.
- The number is between 100 to 200.

What is my number?

Can you help Rexford solve their task?

To help Rexford with their task, the first thing we need to do is find the common multiple of 10 and 7. Hence, by listing all the common multiples of 7 and 10, we will have the numbers 70, 140, 210, 280, 350… and so on.

The next condition says that the number should be between 100 and 200. Thus, from the list, the only number that satisfies the given condition is 140.

Therefore, the number Rexford’s team is looking for is **140**.

See… finding any multiples of ten is not as complicated as you think it was – and so is solving problems involving multiples of 10.

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