# Multiples of 21

Twenty-one is a composite number with proper divisors 1, 3, and 7. It is a triangular, octagonal, and a Fibonacci number. It is considered as a triangular number because the sum of the first 6 counting numbers 1, 2, 3, 4, 5, and 6 is equivalent to 21.

In many cultures, activities, religions, and fields, numbers have distinct symbolism and significance. In order for us to understand the meaning of number 21, we need to discover first the meaning behind numbers 2 and 1. Number 2 is associated with partnerships, cooperation, diplomacy, and trust, whereas number 1 is associated with new beginnings and a hopeful mindset.

Number 21 is a reminder to take care of your own beliefs and thoughts because they are the ones responsible for constructing your own reality. Thinking positively will also attract positive things towards you.

So… are you ready to attract new positive learning? Let’s go as we journey to another magical mathematical lesson about multiples of 21!

## Multiples of 21 are 42, 63, 84, 105, 126, 147, 168, 189 …

Multiples of a number are generated by multiplying a number by another number. Say, for example, the numbers 3, 6, 9, 12, 15, 18, and 21 are all multiples of 3, and can be obtained by simply getting the product of 3 by the integers 1, 2, 3, 4, 5, 6 and 7, respectively.

In essence, we can say that multiples of 21 are the results of multiplying 21 by any integer. Consider the numbers 21, 42, 63, 84, 105, 126, 147, 168, 189, and 210. These numbers are examples of multiples of 21 as this is generated by multiplying 21 by the first ten counting numbers.

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 21.

Now, let us continue our mathematical adventures in finding multiples of 21!

## How to find the multiples of 21?

Now that we’ve properly defined what it means to say that a number is a multiple of 21, let us now determine any multiples of 21. Multiples of 21 can be determined using two methods: repeated addition and multiplication.

**Skip counting**, often known as **repeated addition**, is done by adding 21 as many times as necessary. The diagram below shows how to perform repeated counting.

The first and smallest multiple of a number is any number is the number itself. Hence, the first multiple of 21 is 21.

By repeated addition, to get the 2^{nd} multiple of 21, we will add 21 twice. Thus, $$21\;+\;21\;=\;42$$. Repeatedly adding 21 will generate another number that is a multiple of 21.

Next, the third multiple of 21 can be done by adding 21 thrice. Hence, $$21\;+\;21\;+\;21\;=\;63$$.

It’s a very simple method, isn’t it? But how about finding the 153^{rd} multiple of 21? Are we going to repeatedly add 21 for 153 times? Of course not – that’s why there is another method called **multiplication**!

We have previously defined that a multiple of 21 is generated by multiplying 21 to any integer. In essence, any number that can be expressed in the form **21 n **is a multiple of 21 – where

*n*is an integer.

Say, we want to find the 153^{rd} multiple of 21. To get the 153^{rd} multiple of 21, we will simply get the product of 21 and 153. Hence, $$21\;\times\;153\;=\;3,213$$. Therefore, the 153^{rd }multiple of 21 is 3,213.

Now, how about finding the negative 25^{th} multiple of 21? To determine the negative 25^{th} multiple of 21, multiply 21 by -25. Thus, $$21\;\times\;-25\;=\;-525$$. Therefore, the negative 25^{th }multiple of 21 is –525.

Consider the table below. Listed are the first five multiples of 21 that is generated using repeated addition and multiplication method. Observe how the two methods are different but will always have the same result.

n^{th} Multiple | Repeated Addition | Multiplication |
---|---|---|

1st multiple | 21 | 21 × 1 = 21 |

2nd multiple | 21 + 21 = 42 | 21 × 2 = 42 |

3rd multiple | 21 + 21 + 21 = 63 | 21 × 3 = 63 |

4th multiple | 21 + 21 + 21 + 21 = 84 | 21 × 4 = 84 |

5th multiple | 21 + 21 + 21 + 21 + 21 = 105 | 21 × 5 = 105 |

See… finding multiples of 21 is very straightforward and easy to learn, right?

### Did you know that…

A 21-gun salute is a military honor bestowed on royalty or international leaders? It originated way back in the 17^{th} century. The number 21 came from the tradition of galley ships emptying their cannons as a message of peace to distant ports. When doing the 21-gun salute, the gap between successive guns is 5 seconds.

What does it feel like to have a 21-gun salute? Guess we’ll never know, but this is such an amazing discovery!

## List of First 30 multiples of 21

Integers have an endless number of possibilities. Hence, listing all the possible multiples of 21 is pointless. We have, however, created a list of the first 30 multiples of 21 which is generated by multiplying the integers 1 to 30 by 21.

To start of the list, get the product of 21 and 1, which will be the first multiple of 21. Then, multiply two by 21 to get the 2^{nd} multiple of 21, and so on.

Product of 21 and a positive counting number | Multiples of 21 |
---|---|

21 × 1 | 21 |

21 × 2 | 42 |

21 × 3 | 63 |

21 × 4 | 84 |

21 × 5 | 105 |

21 × 6 | 126 |

21 × 7 | 147 |

21 × 8 | 168 |

21 × 9 | 189 |

21 × 10 | 210 |

21 × 11 | 231 |

21 × 12 | 252 |

21 × 13 | 273 |

21 × 14 | 294 |

21 × 15 | 315 |

21 × 16 | 336 |

21 × 17 | 357 |

21 × 18 | 378 |

21 × 19 | 399 |

21 × 20 | 420 |

21 × 21 | 441 |

21 × 22 | 462 |

21 × 23 | 483 |

21 × 24 | 504 |

21 × 25 | 525 |

21 × 26 | 546 |

21 × 27 | 567 |

21 × 28 | 588 |

21 × 29 | 609 |

21 × 30 | 630 |

## Solving problems involving multiples of 21

Now, let’s try solving some word problems that we may encounter in our daily lives. Are you ready?

**Problem #1**

Danerie bought a food pack for $21 to donate to typhoon victims. If he bought 345 food packs, how much did Danerie spend?

We are asked to find the total amount Danerie spent on buying food packs. Each food pack costs $21 and Danerie bought 345 of it. So, to get the total amount of money he spent, we need to find the 345^{th} multiple of 21. This can be done by getting the product of 21 and 345. Hence, $$\$21\;\times\;345\;=\;\$7,245$$.

Therefore, Danerie spent $7,245 on food packs to donate to the typhoon victims. He is one generous gentleman, isn’t he?

Now, let’s help Hadji solve his problem!

**Problem #2**

Hadji has 3,500 lego pieces. Can he group them in stacks of 21 lego equally?

In this problem, we are asked to determine if it is possible to equally group 3,500 lego pieces by 21. For it to be equally distributed, 3,500 must be a multiple of 21. Now, to determine if 3,500 is a multiple of 21, we must get its quotient and see if it will give us a result of zero remainder.

Hence, $$3,500\;\div\;21\;=\;\frac{500}3$$ or 166.67. Since the quotient is not an exact number, we can conclude that it is not possible to equally stack the lego by 21.

Now, let’s see if you have learned something today by answering these 3 short questions!