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Multiples of 13

Multiples of 13 are whole numbers. They are the product of n natural numbers and 13. In other words, we can say that the multiples of 13 are the numbers that can be divided by 13 without leaving any remainder. We can create n number of multiples of 13 just by multiplying 13 with n natural numbers. In this mini-lesson, we will calculate the multiples of 13 and we will learn some interesting facts about these multiples.

First five multiples of 13:13, 26, 39, 52, and 65
Prime factorization of 13:13 = 1 × 13

1.	What Are the Multiples of 13?
2.	First 20 Multiples of 13
3.	Tips and Tricks
4.	FAQs on Multiples of 13

What Are the Multiples of 13?

Multiples of 13 are derived by multiplication of 13 with whole numbers. We can find out the multiples of 13 using its division facts as well. For example, division facts for the multiples of 13 are: 39 ÷ 13 = 3, 52 ÷ 13 = 4, 65 ÷ 13 = 5. This will give us multiples of 13 as well as factors of 13. We will consider only those number which are exactly divisible by 13 without leaving any remainder behind. Can you think of any other number with the help of which we can find multiples of 13? Let us try to derive multiples of 13 using multiples of 3. To obtain the multiples of 13, add natural numbers to the ten's digit of the multiples of 3. Hence, the first 10 multiples of 13 are obtained as follows: (1+0)3, (2+0)6, (3+0)9, (4+1)2, (5+1)5, (6+1)8, (7+2)1, (8+2)4, (9+2)7, (10+3)0 = 13, 26, 39, 52, 65, 78, 91, 104, 117, 130.

First 10 Multiples of 13
13 × 1 = 13	13 × 6 = 78
13 × 2 = 26	13 × 7 = 91
13 × 3 = 39	13 × 8 = 104
13 × 4 = 52	13 × 9 = 117
13 × 5 = 65	13 × 10 = 130

Hence, the first 10 multiples of 13 are 13, 26, 39, 52, 65, 78, 91, 104, 117, and 130.

First 20 Multiples of 13

The first 20 multiples of 13 are those numbers which we obtain as the result when we multiply natural numbers from 1-20 with 13. We just derived first 10 multiples of 13. Let us try same trick to derive multiples of 13 using multiples of 3 for natural numbers 11-20. The first 20 multiples of 13 can also be obtained using a skip count method. The first 20 multiples of 13 are listed in the table below.

Multiples of 13 from 11 to 20
13 × 11 = 143	13 × 16 = 208
13 × 12 = 156	13 × 17 = 221
13 × 13 = 169	13 × 18 = 234
13 × 14 = 182	13 × 19 = 247
13 × 15 = 195	13 × 20 = 260

To understand the concept of finding multiples, let us take a few more examples.

Multiples of 12 - The first five multiples of 12 are 12, 24, 36, 48, and 60.
Multiples of 3 - The first five multiples of 3 are 3, 6, 9, 12, and 15.
Multiples of 10 - The first five multiples of 10 are 10, 20, 30, 40, and 50.
Multiples of 14 - The first five multiples of 14 are 14, 28, 42, 56, and 70.
Multiples of 11 - The first five multiples of 11 are 11, 22, 33, 44, and 55.

Tips and Tricks:

We can derive multiples of 13 with the help of multiples of 3.
To obtain the multiples of 13, add natural numbers to the ten's digit of the multiples of 3.
We can use skip counting method also to find multiples of 13 as shown in image below.

Challenging Questions:

Solve the following on the basis of your understanding about multiples of 13.

Find the sum of first 10 odd multiples of 13.
Find the average of first 20 multiples of 13.

Example 1: If Jack presses the doorbell 1 time, it rings 5 times. Using the multiples of 13, find how many times does the bell ring when it is pressed 13 times?.

Solution:

Number of times the bell rings when pressed once = 5
Therefore, number of times the bell rings when pressed 13 times = 13 × 5 = 65
Hence, the bell will ring 65 times.
Here, 65 is the 5th multiple of 13.
Example 2: Ria's mother has to pay the amount "13 less than 13 times of 13" in dollars. Using the multiples of 13, find how much is she required to pay?.

Solution:

13 less than 13 times of 13 = 13 × 13 - 13 = 156
Hence, Ria's mother needs to pay $156.

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FAQs on Multiples of 13

How do you find the multiples of 13?

Multiply any natural number with 13. For example, 13 × 2 = 26
26 is the 2nd multiple of 13.

What are the first 5 multiples of 13?

The first 5 multiples of 13 are 13, 26, 39, 52, and 65.

Are all multiples of 13 even?

No, all the multiples of 13 are not even. Some multiples of 13 are even and some are odd.
For example, 13 × 1 = 13; 13 is odd number.
13 × 2 = 26; 26 is even number.

What is the least common multiple of 13 and 133?

Here, we have to take factors of both the numbers first.
13 = 13 × 1
133= 7 × 19
Hence, the least common multiple of the numbers 13 and 133 is 13 × 7 × 19 = 1729

What are the first 10 multiples of 13?

The first 10 multiples of 13 are 13, 26, 39, 52, 65, 78, 91, 104, 117, and 130.

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