# Multiples of 20

**A pronic number** is a number wherein it is produced by the product of two consecutive integers in the form,$$n(n\;+\;1)$$.

**Twenty** is an example of a pronic number since it is a product of 4 and 5. Not only that, but it is also considered as a **tetrahedral number** like 1, 4, and 10.

Twenty is indeed a special number as it is also used in a vigesimal number system – a number system which is in base 20. Now, are you ready to take a deeper understanding of this special number called twenty?

If so, let’s start our adventure in learning more about 20 and its multiple!

## Multiples of 20 are -40, -20, 0, 20, 40, 60, 80, 100

**Multiples of twenty** are numbers that can be divided by 20 without leaving any remainder. More so, if a number is *n*-times of 20 or a number is generated by multiplying any integer such as 1, 2, 3, 4, … and so on, we can definitely say that it is a multiple of 20.

0 is a multiple of 20, because if $$20\;\times\;0\;=\;0$$.

In this case, *n* is 0. 100 is also a multiple of 20 because $$20\;\times\;5\;=\;100$$, where *n* is 5.

A sequence of multiples of 20 is a series of numbers in which the difference between two consecutive numbers is always 20. Consider the following sequence:

**-40, -20, 0, 20, 40, 60, 80, 100**

Did you notice something? Multiples of any number can be a positive or negative number as integer ranges from negative to positive infinity. More so, the difference between two consecutive numbers is always 20.

## How to find the multiples of 20?

Now that we’ve defined what it means to say a number is a multiple of 20. It is now time for us to figure out how to find any possible multiples of 20. There are two ways where we can find multiples of 20: **repeated addition** and **multiplication**.

**Skip counting** or **repeated addition** is accomplished by repeatedly adding 20 as many times as necessary. The diagram below explains how to do repeated counting.

The first multiple of 20 is the number itself. Hence, to start with repeated addition, we will start with 20.

Now, to find the 2^{nd} multiple of 20, we need to add 20 twice. Hence, $$20\;+\;20\;=\;40$$.

Therefore, the 2^{nd} multiple of 20 is 40.

More so, if we are asked to find the 10^{th} multiple of 20 using repeated addition, we need to add 20 ten times. Hence, the 10^{th} multiple of 20 can be determined by $$20\;+\;20\;+\;20\;+\;20\;+\;20\;+\;20\;+\;20\;+\;20\;+\;20\;+\;20\;=\;200$$.

Therefore, the 10^{th} multiple of 20 is 200.

Repeated addition can be time-consuming especially when we are asked to get the 500^{th} multiple of 20 or even the 100^{th} multiple of it. Hence, the need to learn the second method which is multiplication.

Since multiples of 20 can be expressed by 20*n*, where *n* is any integer, then we can simply get the product of 20 and any number to determine its multiple.

Say, for example, we are asked to get the 5^{th} multiple of 20. By repeated addition, we can do this by doing$$20\;+\;20\;+\;20\;+\;20\;+\;20\;=\;100$$. But by getting the product of 20 and 5, we will have $$20\;\times\;5\;=\;100$$.

Both methods will have the same result, but it will depend on how fast you will arrive at the answer.

Now, let’s try to determine the 37^{th} multiple of 20. Since we are asked to get the 37^{th} multiple of 20, we will use the multiplication method. Thus, $$20\;\times\;37\;=\;740$$.

Therefore, the 37^{th} multiple of 20 is 740.

It’s nice to learn the two methods in finding any multiples of 20, right?

Observe the table below. We’ve listed the first five multiples of 20 and how we can find them using the repeated addition and multiplication method.

nᵗʰ Multiple | Repeated Addition | Multiplication |
---|---|---|

1ˢᵗ multiple | $$20$$ | $$20\;\times\;1\;=\;20$$ |

2ⁿᵈ multiple | $$20\;+\;20\;=\;40$$ | $$20\;\times\;2\;=\;40$$ |

3ʳᵈ multiple | $$20\;+\;20\;+\;20\;=\;60$$ | $$20\;\times\;3\;=\;60$$ |

4ᵗʰ multiple | $$20\;+\;20\;+\;20\;+\;20\;=\;80$$ | $$20\;\times\;4\;=\;80$$ |

5ᵗʰ multiple | $$20\;+\;20\;+\;20\;+\;20\;+\;20\;=\;100$$ | $$20\;\times\;5\;=\;100$$ |

## List of First 30 multiples of 20

There are an infinite number of integers. As a result, listing all of the possible multiples of 20 is pointless. However, we’ve compiled a list of the first 30 multiples of 20 that is generated by multiplying the numbers 1 to 30 by 20.

To make a list of multiples of 20, multiply 20 by one to get the first multiple of 20, 20, then multiply 20 by two to get the second multiple of 20, 40, then multiply 20 by three to get the third multiple of 20, 60, and so on.

Product of 20 and a positive counting number | Multiples of 20 |
---|---|

$$20\;\times\;1$$ | 20 |

$$20\;\times\;2$$ | 40 |

$$20\;\times\;3$$ | 60 |

$$20\;\times\;4$$ | 80 |

$$20\;\times\;5$$ | 100 |

$$20\;\times\;6$$ | 120 |

$$20\;\times\;7$$ | 140 |

$$20\;\times\;8$$ | 160 |

$$20\;\times\;9$$ | 180 |

$$20\;\times\;10$$ | 200 |

$$20\;\times\;11$$ | 220 |

$$20\;\times\;12$$ | 240 |

$$20\;\times\;13$$ | 260 |

$$20\;\times\;14$$ | 280 |

$$20\;\times\;15$$ | 300 |

$$20\;\times\;16$$ | 320 |

$$20\;\times\;17$$ | 340 |

$$20\;\times\;18$$ | 360 |

$$20\;\times\;19$$ | 380 |

$$20\;\times\;20$$ | 400 |

$$20\;\times\;21$$ | 420 |

$$20\;\times\;22$$ | 440 |

$$20\;\times\;23$$ | 460 |

$$20\;\times\;24$$ | 480 |

$$20\;\times\;25$$ | 500 |

$$20\;\times\;26$$ | 520 |

$$20\;\times\;27$$ | 540 |

$$20\;\times\;28$$ | 560 |

$$20\;\times\;29$$ | 580 |

$$20\;\times\;30$$ | 600 |

## Did you know that…

In the game of chess, there are exactly 20 different moves that you can legally make at the start of the game? Whether you move the pawns one or two step forward or the knights, there can only be 20 legally moves at the beginning of the game!

What an awesome discovery!

## Solving problems involving multiples of 20

**Problem #1**

Edward sells video games for $20 each. If he already sold 67 video games, how much is his total earnings?

In the given problem, we are asked to get the total earnings Edward got after selling 67 video games.

Since the cost of each video game is $20, we can get his total earnings by getting the 67^{th} multiple of 20. Hence, we can do this by getting the product of 20 and 67.

Thus, $$\$20\;\times\;67\;=\;\$1,340$$.

Therefore, Edward earned **$1,340** from selling 67 video games at $20 each!

Now, let’s help Venus determine the total number of eggs she will harvest.

**Problem #2**

Every week, Venus harvests 20 chicken eggs and 20 ostrich eggs. What is the total number of eggs will she harvest after 13 weeks?

It is stated that Venus harvests 20 chicken eggs and 20 ostrich eggs every week. Since we need to find the total number of eggs she was able to harvest for 13 weeks, we need to get the 13^{th} multiple of 20. Hence, we need to get the product of 20 and 13.

Thus, $$20\;chicken\;eggs\;\times\;13\;=\;260\;chicken\;eggs$$. Since she also harvests 20 ostrich eggs each week, we also need to find the total number of ostrich eggs she gathered. Hence, $$20\;ostrich\;eggs\;\times\;13\;=\;260\;ostrich\;eggs$$.

Now, to get the total number of eggs she collected, all we need to do is add the total number of chicken eggs and ostrich eggs. Thus, **260 + 260 = 520 eggs**.

Therefore, the total number of collected eggs after 13 weeks is **520 eggs**.

Now, let us try to apply the knowledge we’ve learned in answering these 3 short quizzes!