Multiples of 13

Most people are afraid of the number 13 because it means bad luck, especially on
Friday the 13^th. The fear of people in this number can be traced back to religious
believes – particularly Christianity.

This can actually be seen in the illustration of the “Last Supper” during Jesus’ last meal with his 12 disciples, and Judas being the 13th apostle that will betray Jesus. The number 13 was then associated with the agony of Jesus, who was crucified the following day.

More so, some condominiums and hotels skip putting 13^th floor. For them, the 13^th floor doesn’t exist as it will not be sold to some potential buyers. On the other hand, Taylor Swift considered 13 as her lucky number.

Swifties probably know the reason why – aside from the fact that she was born on December 13, 1989, her first debut album was on top for 13 weeks.

Furthermore, every time she is seated in row M (13^th letter) or row 13 during an awards night, she’s certain that she will get that trophy!

Some numbers may be unlucky for some, but luck really depends on how we see it.
And we are certainly lucky to learn more things about 13, aren’t we? Now, let’s ride this getaway car and remember how gorgeous this 13 and it's multiple are!

Multiples of 13 are 13, 26, 39, 52, 65, 78, 91 ...

Multiples of 13 are numbers that when divided by 13, will get an exact number or a number with zero remainders. Simply, it is the product of 13 and any integer. Thus, we can say that when a random number is expressed as 13n, we already know that it is a multiple of 13.

We can also say that if a sequence where the difference between consecutive numbers is 13, it is a multiple of 13.

How to find the multiples of 13?

One method for determining multiples of 13 is to skip count by 13. This is accomplished by simply adding 13 as many times as you desire. For example, to find the first five multiples of 13, we begin with the number itself – 13.

Then we'll add another 13 to get the next number. As a result, we will have 13 + 13 = 26.
If we continue down this path, we will have the same result as the diagram below.

This method is excellent if we are to find a small n^th multiple of a number such as finding the first 5 or 10 multiples of 13… but it is not the most convenient way to find the 15678^th or 99999^th multiple of 13.

This is where multiplication comes in! Multiplication is our life-saver in finding large nth multiples of 13. Since we have defined a multiple of 13 as a product of two numbers that can be expressed as 13n, we will easily use this method to find any multiples of 13.

For example, we are asked to find the 67th positive multiple of 13; we will multiply 13 by 67.

Hence, $$\mathbf{13}\boldsymbol\;\boldsymbol\times\boldsymbol\;\mathbf{67}\boldsymbol\;\boldsymbol=\boldsymbol\;\mathbf{871}$$. It is so simple, right?

Let’s try another one. Suppose we are looking for the 889^th multiple of 13. Getting the product of 13 and 889 will give us the result of 11,557.

See how convenient multiplication is in determining multiples of 13? Now let’s take a look at the table. The table below shows the result of skip counting and multiplying 1 to 5 and 13.

nth Multiple	Skip Counting	Multiplication
1st multiple	13	13 x 1 = 13
2nd multiple	13 + 13 = 26	13 x 2 = 26
3rd multiple	13 + 13 + 13 = 39	13 x 3 = 39
4th multiple	13 + 13 + 13 + 13 = 52	13 x 4 = 52
5th multiple	13 + 13 + 13 + 13 + 13 = 65	13 x 5 = 65

Did you know that…

The word triskaidekaphobia is for people who suffer from the fear of the number 13? Stephen King, a famous writer, has this phobia wherein he skips the 13th step of a staircase, becomes uneasy watching shows on Channel 13 – or even skipping pages 13 and pages when added up to 13, such as pages 94 and 193.

Are you also scared of the number 13?

List of First 30 multiples of 13

It is not wise to list all multiples of 13, because this will probably contain an infinite number of thirteen multiples. This is why the multiplication table is limited to the first 30 multiples of 13.

Product of 13 and a positive counting number	Multiples of 13
$$13\times1$$	13
$$13\times2$$	26
$$13\times3$$	39
$$13\times4$$	52
$$13\times5$$	65
$$13\times6$$	78
$$13\times7$$	91
$$13\times8$$	104
$$13\times9$$	117
$$13\times10$$	130
$$13\times11$$	143
$$13\times12$$	156
$$13\times13$$	169
$$13\times14$$	182
$$13\times15$$	195
$$13\times16$$	208
$$13\times17$$	221
$$13\times18$$	234
$$13\times19$$	247
$$13\times20$$	260
$$13\times21$$	273
$$13\times22$$	286
$$13\times23$$	299
$$13\times24$$	312
$$13\times25$$	325
$$13\times26$$	338
$$13\times27$$	351
$$13\times28$$	364
$$13\times29$$	377
$$13\times30$$	390

Solving problems involving multiples of 13

Now that we’ve discussed the definition and process of finding multiples of 13, it is now time to apply it in solving real-life problems!

Problem #1

Zack has been preparing his Christmas presents for the street children since the start of December. For the past nine days, he has been buying random toys that is in the sequence 13, 26, 39… and so on. How many gifts does Zack plan to give to the homeless kids?

To solve the total number of gifts Zack plans to give, observe that as the day goes by, the number of toys he buys has a constant increase of 13. Hence, we can say that it is a sequence of multiples of 13.

Since it is a sequence of multiples of 13, we need to find the number of presents he
bought for the past 9 days. Thus, we will have the sequence 13, 26, 39, 52, 65, 78, 91, 104, and 117.

Now, we are asked to get the total number of presents he prepared for the kids. So, we are going to add these numbers. Thus,

13 + 26 + 39 + 52 + 65 + 78 + 91 + 104 + 117 = 585

Therefore, Zack plans to give away 585 Christmas presents for the homeless kids.
What a lovely heart Zack has!

Now, let’s try if we can solve the next problem.

Problem #2

Suppose Taylor released 13 albums already – and within each album contains 13 songs that can be played for exactly 13 minutes. What is the total number of minutes you can listen to all her albums?

We are asked to find the total number of minutes it will take us to finish all the 13 albums Taylor has released. It was stated that every album contains 13 songs, and each of those songs will take 13 minutes to complete. Hence, we just need to get the
product 13 albums, 13 songs, and 13 minutes.

Thus,   $$\mathbf{13}\boldsymbol\;\boldsymbol\times\boldsymbol\;\mathbf{13}\boldsymbol\;\boldsymbol\times\boldsymbol\;\mathbf{13}\boldsymbol\;\boldsymbol=\boldsymbol\;\mathbf2\boldsymbol,\mathbf{197}$$.

Therefore, we can finish all 13 albums in 2,197 minutes. That’s a lot of minutes, but we’re pretty sure we can remember all her songs all too well!

Finding the multiples of 13 is fun, huh? Now, let’s answer the three practice problems in style!

Take a quiz

Question 1Recognize multiples of 13

What are the first five positive multiples of 13?

Answer

13, 26, 39, 52, 65.

They are found by multiplying 13 by 1, 2, 3, 4, and 5.

Question 2Continue the sequence

What comes after 65 in the sequence of positive multiples of 13?

Answer

78.

Add 13 to 65.

Question 3Check a multiple

Is 104 a multiple of 13?

Answer

Yes. 104 = 13 × 8.

A number is a multiple when it is the product of the original number and an integer.