# Multiples of 14

Couples and the hopeless romantic ones may choose 14 as their favorite number – because why not? Valentine’s Day is celebrated every 14^{th} of February. In some parts of the world, it is a day of sending love cards, flowers, and chocolates. It is also a day for the hopeless romantics to confess their feelings.

More so, **fourteen** represents sacrifice and generosity in some religions. However, in China, 14 is considered an unlucky number because it is pronounced as “one four,” which sounds like “want to die” in the Chinese language.

Now, let’s see how you will see the number 14 as we discuss this romantic but mysterious number and its multiples. Are you ready for some sweet treats?

## Multiples of 14 are 14, 28, 42, 56, 70, 84 …

When we say that a number is a multiple of 14, it means that every time we divide a number with any positive or negative integer, the result will always be a whole number. In essence, any number that can be expressed as * 14n* is a multiple of 14 – where

**is an integer.**

*n*Let’s look at this sequence of numbers!

-70, -56, -42, -28, -14, 0, 14, 28, 42, 56, 70

Do you observe something similar on the two consecutive numbers? If we look at the difference of 28 and 14, the result is 14. Similarly, if we add 14 to -56, the answer is -42. Hence, we can say that a sequence of numbers are multiples of 14 if the sum or difference of two consecutive numbers is always 14.

But what if the sequence goes like this – **14**,** 21**,** 28**,** 42**

Can we say that it is also a sequence of numbers that are multiples of 14?

The answer is **NO**. Even though the difference between 42 and 28 is 14, numbers 14 and 21 are not 14.

## How to Find the Multiples of 14?

Now that we have established what it means to state a number is a multiple of 14. Now we’ll figure out how to find all of the possible multiples of 14. We can determine the multiples of 14 in two ways – repeated addition or multiplication.

Skip counting or repeated counting is done by adding 14 as many times as possible. The figure below shows how repeated counting can be done.

14 is the first multiple of 14. Hence, to get the second multiple by skip counting, we need to add 14. Thus, $$14\;+\;14\;=\;28$$ .

Similarly, for us to get the 3^{rd} multiple of 14 by skip counting, we need to add another 14. Hence, $$14\;+\;14\;+\;14\;=\;42$$ .

Can you continue adding 14 to get the 4^{th} and 5^{th} multiples of 14 and compare if you will have the same result as the diagram?

Another way to find multiples of 14 is by multiplication. We have said earlier that a number that can be expressed as *14n* is a multiple of 14. So, if we assume that *n* is a counting number, we need to get the product of 14 and *n*.

Say you want to find the 17^{th} multiple of 14; all we need to do is multiply 14 by 17. Thus, **$$14\;\times\;17\;=\;238$$** . Therefore, the 17th multiple of 14 is 238!

Let’s try getting the 19^{th} negative multiple of 14. Since we are asked to get the 19^{th} negative multiple of 14, we will multiply 14 by -19. Hence, **$$14\;\times\;-19\;=\;-266$$** .

Here’s what we know so far, skip counting and multiplication are two methods we can use to find any multiples of 14. The table below shows how the two methods.

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

1^{st} multiple | 14 | 14 x 1 = 14 |

2^{nd} multiple | 14 + 14 = 28 | 14 x 2 = 28 |

3^{rd} multiple | 14 + 14 + 14 = 42 | 14 x 3 = 42 |

4^{th} multiple | 14 + 14 + 14 + 14 = 56 | 14 x 4 = 56 |

5^{th} multiple | 14 + 14 + 14 + 14 + 14 = 70 | 14 x 5 = 70 |

## List of First 30 Multiples of 14

There are infinitely many positive and negative integers. Hence, it makes no sense to list all the possible multiples of 14. But, we’ve made a list of the first 30 multiples of 14, so you can double-check if we got the same result in multiplying 14 to numbers 1 to 30.

Product of 14 and a positive counting number | Multiples of 14 |
---|---|

14 x 1 | 14 |

14 x 2 | 28 |

14 x 3 | 42 |

14 x 4 | 56 |

14 x 5 | 70 |

14 x 6 | 84 |

14 x 7 | 98 |

14 x 8 | 112 |

14 x 9 | 126 |

14 x 10 | 140 |

14 x 11 | 154 |

14 x 12 | 168 |

14 x 13 | 182 |

14 x 14 | 196 |

14 x 15 | 210 |

14 x 16 | 224 |

14 x 17 | 238 |

14 x 18 | 252 |

14 x 19 | 266 |

14 x 20 | 280 |

14 x 21 | 294 |

14 x 22 | 308 |

14 x 23 | 322 |

14 x 24 | 336 |

14 x 25 | 350 |

14 x 26 | 364 |

14 x 27 | 378 |

14 x 28 | 392 |

14 x 29 | 406 |

14 x 30 | 420 |

## Did you know that…

If a number is both divisible by 2 and 7 – you can easily say that it is also a multiple of 14? Let’s try to see if it’s real, shall we?

Suppose 714 is a multiple of 14.

First, we need to check if it is really a multiple of 14. Thus, **$$714\;\div\;14\;=\;51$$** .

Then, it should be a multiple of 2 – and since it is an even number, we can definitely say that it is a multiple of 2. Now, all we need to do is to check if it is also divisible by 7. Hence, **$$714\;\div\;7\;=\;102$$** . So, we now know that it is also divisible by 7.

Since it is both divisible by 2 and 7, then we are confident that it is divisible by 14!

What a quick trick to see if numbers are multiples of 14, right?

## Solving Problems Involving Multiples of 14

Now, let’s put your learning into a different kind of fun! Let’s work on these two problems.

**Problem #1**

Philip hired a tutor for his daughter, Samantha. Every week, Samantha’s tutor needs to teach her for 14 hours. Her tutor is paid $14 per hour. How much would her tutor earn at the end of the 14^{th} week?

The problem asks us to compute the tutor’s earning after 14 weeks of teaching Samantha. It is also stated that every hour, the tutor earns $14 an hour and needs to work 14 hours a week. Thus, to get the total tutor’s earning, let’s compute first how much she earns each week. So, $$\$14\;\times14\;hours\;=\;\$196$$.

Then, to get the total earnings of the tutor, we need to multiply the total number of weeks she needs to teach Samantha. Hence, $$\$196\;\times14\;weeks\;=\;\$2,744$$.

Therefore, Samantha’s tutor will earn $2,744 after 14 weeks.

It’s an easy problem, isn’t it? Now, let’s try another one!

**Problem #2**

Sean bought 14 flowers for his teachers, 14 chocolates for his friends, and 14 mini cakes for his family. How many flowers and sweets did Sean buy?

In the given problem, it is stated that Sean bought 14 flowers, 14 chocolates, and 14 mini cakes. Thus, to find the total number of flowers and sweets Sean bought, we are going to add 14 repeatedly. Hence,**14 flowers + 14 chocolates + 14 mini cakes = 42**

We can also use the multiplication method by finding the 3rd multiple of 14. So, $$14\;\times\;3\;=\;42$$ .

Therefore, Sean bought a total of **42 flowers and sweet treats**!

See, finding and solving problems involving multiples of 14 is as sweet as eating chocolates!