# What are the Multiples of 7?

**Seven** is considered a lucky number in many cultures around the world. For some, the number seven represents completeness and perfection. More so, in Pythagorean numerology, 7 represents spirituality.

This is because it comprises 4 and 3, which are physical and spiritual numbers, respectively. Not only does the number seven signify the jackpot on slot machines, but it is also significant for countless stories and folklore, religion, and philosophy.

It is no surprise why most people are drawn into the number 7. Are you getting excited to see the remarkable side of 7 and its multiples?

## Multiples of are 77, 14, 21, 28, 35, 42, 49 …

A **multiple of 7** is a numerical value formed by multiplying one natural number by another natural number or counting number. Do you notice something on the numbers above?

If you observe the numbers 7, 14, 21, 28, 32…, the difference between two consecutive numbers is always 7. Say **$$21\;-\;14\;=\;7$$** , and **$$35\;-\;28\;=\;7$$** .

Amazing, right?

They are called multiples of 7 because every time we divide a number by 7, it will give us a remainder of zero.

Thus, to say that a number is a multiple of 7, it should be in the form of ** 7n** where

**is any natural number. In a nutshell, a multiple of 7 is formed when we multiply 7 by any counting number.**

*n*Now, let’s dive further into determining the multiples of 7.

## How to Find the Multiples of 7?

Finding the multiples of 7 can be done by **skip counting** or **repeated addition** and **multiplication**.

Let’s try to determine the first five multiples of 7 by repeated addition.

To get the first five multiples of 7, we will start by its smallest multiple – which is itself. Then, if we add another 7 to 7, we will have **$$7\;+\;7\;=\;14$$** . Continuing this process, we will have **$$14\;+\;7\;=\;21$$** .

Doing this five times will give us the first five multiples of 7 as 7, 14, 21, 28, and 35.

What a great way to find the multiples of 7, right? Now, let’s try another method for finding multiples of 7.

**Multiplication** is the “short-cut method” of repetitive addition. We have defined a multiple of 7 as a number that can be defined as * 7n* where

*is any natural number.*

**n**For example, if you are asked what the 18^{th} multiple of 7 is, the easiest way to do it is by multiplying 7 by 18. Thus, **$$7\;\times\;18\;=\;126$$** .

Let’s try another example. What is the 49^{th} negative multiple of 7?

To find the 49^{th} negative multiple of 7, we will simply multiply 7 by -49. Hence, **$$7\;\times\;-49\;=\;-343$$** . Therefore, the 49^{th} negative multiple of 7 is –343.

The table below shows the result if we do skip counting and multiplication. Multiplication is the simplest way to find the multiples of 7. Skip counting, on the other hand, is a fun way to determine multiples.

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

1^{st} multiple | 7 | 7 x 1 = 7 |

2^{nd} multiple | 7 + 7 = 14 | 7 x 2 = 14 |

3^{rd} multiple | 7 + 7 + 7 = 21 | 7 x 3 = 21 |

4^{th} multiple | 7 + 7 + 7 + 7 = 28 | 7 x 4 = 28 |

5^{th} multiple | 7 + 7 + 7 + 7 + 7 = 35 | 7 x 5 = 35 |

## List of First 30 Multiples of 7

The table below shows the first 30 positive multiples of 7. We cannot list all the possible multiples of 7 as there are infinitely many natural numbers. Thus, there are also infinitely many multiples of 7.

Product of 7 and a positive counting number | Multiples of 7 |
---|---|

7 x 1 | 7 |

7 x 2 | 14 |

7 x 3 | 21 |

7 x 4 | 28 |

7 x 5 | 35 |

7 x 6 | 42 |

7 x 7 | 49 |

7 x 8 | 56 |

7 x 9 | 63 |

7 x 10 | 70 |

7 x 11 | 77 |

7 x 12 | 84 |

7 x 13 | 91 |

7 x 14 | 98 |

7 x 15 | 105 |

7 x 16 | 112 |

7 x 17 | 119 |

7 x 18 | 126 |

7 x 19 | 133 |

7 x 20 | 140 |

7 x 21 | 147 |

7 x 22 | 154 |

7 x 23 | 161 |

7 x 24 | 168 |

7 x 25 | 175 |

7 x 26 | 182 |

7 x 27 | 189 |

7 x 28 | 196 |

7 x 29 | 203 |

7 x 30 | 210 |

## Did you know that…

The number 7 is significantly common in nature than most of us realize?

There are

seven oceans,seven continents, andseven colors in the rainbow. The Earth was also created inseven days, including the rest day.

This explains why if people are asked their favorite number from 1 to 10, they usually answer 7.

Seven is indeed a remarkable number. Can you think of other things that make seven an interesting number?

## Problems Involving Multiples of 7

Multiples of 7 are just not a list of numbers that we need to memorize – they can also help us solve real-life problems. Let’s try to solve two problems that involve using multiples of 7.

### Problem #1

Adrian’s new year’s resolution is to save $7 on the first week, $14 on the second week, $21 on the third, $28 on the fourth, and so on. How much does Adrian need to save on the 27^{th} week?

As stated in the problem, Adrian plans to start his savings with $7 on the first week, $14 on the second, $21 on the third, and so on. Observing the increase in his savings, we can notice his saving increases by $7 each week. Hence, to find the amount of money he plans to save on the 27^{th} week, we need to solve for the 27^{th} multiple of 7.

To solve for the 27^{th}, we need to multiply 27 by 7. Thus,

**$$7\;\times\;27\;=\;189$$**

Therefore, on the 27^{th} week, Adrian needs to save **$189**.

Now, let’s try another problem.

### Problem #2

Pierre has 3 baskets of different fruits. The first basket contains 14 bananas, the second basket contains 28 apples, and the third one has 39 cherries. Can Pierre sort all the fruits in each basket into groups of 7?

The problem asked us to sort the fruits in each basket in groups of 7. To solve this problem, we need to check if the number of fruits in each basket is divisible by 7. Let’s start by dividing 14 by 7. Thus, **$$14\;\div\;7\;=\;2$$** . Since 14 is a multiple of 7, we can sort the bananas into groups of 7.

Now, let’s try to do the same process on the baskets of apples and cherries. Dividing 28 by 7, we will have **$$28\;\div\;7\;=\;4$$** . Since 28 is also divisible by 7, we can say that it is also a multiple of 7. Thus, we can sort the apples into groups of 7.

On the basket of cherries, we have a total number of 21 cherries. Hence, dividing it by 7 will result to **$$39\;\div\;7\;=\;5$$** **with a remainder of 4**. Since the result we got has a remainder of 4, this means that 39 is not a multiple of 7. Thus, we cannot sort the cherries into groups of 7.

Therefore, Pierre can sort the bananas and apples into groups of 7, but he will not be able to sort the cherries into exact groups of 7.