Multiples of 7 | Definition, Examples, List, Number Grid, Finding

Introduction

7 is the first multiple of seven, followed by 14, 21, 28, and 35. Multiples of seven are defined as numbers that can be divided by seven precisely without leaving any remainder.

We will learn more about multiples of seven in this article, as well as the list of multiples of seven, how to find multiples of seven, and solutions to frequently asked multiples of seven questions.

What are multiples of 7?

Definition

Numbers that can be divided by seven precisely without any remainder are said to be multiples of seven.

The first few multiples of 7 are the answer to the seven times table.

Seven Times Table

1 × 7 = 7

2 × 7 = 14

3 × 7 = 21

4 × 7 = 28

5 × 7 = 35

6 × 7 = 42

7 × 7 = 49

8 × 7 = 56

9 × 7 = 63

10 × 7 = 70

11 × 7 = 77

12 × 7 = 84

13 × 7 = 91

14 × 7 = 98

15 × 7 = 105

Let us say, for example, 5 × 7 = 35; the fifth multiple of seven is thirty-five. In 9 × 7 = 63, the ninth multiple of seven is sixty-three. The table below shows the first twelve multiples of seven.

Seven Times Table

first multiple of 7 = 7

second multiple of 7 = 14

third multiple of 7 = 21

fourth multiple of 7 = 28

fifth multiple of 7 = 35

sixth multiple of 7 = 42

seventh multiple of 7 = 49

eighth multiple of 7 = 56

ninth multiple of 7 = 63

tenth multiple of 7 = 70

eleventh multiple of 7 = 77

twelfth multiple of 7 = 84

thirteenth multiple of 7 = 91

fourteenth multiple of 7 = 98

fifteenth multiple of 7 = 105

There are infinite multiples of seven. Any number created by multiplying 7 is a multiple of 7. Since 0 × 7 = 0, 0 is also a multiple of 7.

Start counting from zero and keep adding 7 to find multiples of 7. To find the following multiple of 7, add 7 to the multiple you already know.

List of Multiples of 7

The table below shows the multiples of 7 less than 1000.

7	14	21	28	35	42	49	56	63	70
77	84	91	98	105	112	119	126	133	140
147	154	161	168	175	182	189	196	203	210
217	224	231	238	245	252	259	266	273	280
287	294	301	308	315	322	329	336	343	350
357	364	371	378	385	392	399	406	413	420
427	434	441	448	455	462	469	476	483	490
497	504	511	518	525	532	539	546	553	560
567	574	581	588	595	602	609	616	623	630
637	644	651	658	665	672	679	686	693	700
707	714	721	728	735	742	749	756	763	770
777	784	791	798	805	812	819	826	833	840
847	854	861	868	875	882	889	896	903	910
917	924	931	938	945	952	959	966	973	980
987	994

There are infinite multiples of seven. Any number created by multiplying 7 is a multiple of 7. So, to continue the list above, we may multiply the counting numbers by seven or add 7 to the last number, which is a multiple of 7.

Multiples of 7 Number Grid

The table below shows the multiples of 7 on a number grid. The number grid is a helpful tool to use because this involves adding 7 to the previous number. As for the grid below, it starts with seven and then counts seven squares to find the next multiple of 7. The red squares are multiples of 7.

From the number grid above, we may identify the multiples of 7 up to 100 and multiples of 7 up to 200.

Multiples of 7 up to 100

There are 14 multiples of 7 less than 100. These numbers include the following:

7	14	21	28	35	42	49
56	63	70	77	84	91	98

Multiples of 7 up to 200

There are 28 multiples of 7 less than 200. These numbers include the following:

7	14	21	28	35	42	49
56	63	70	77	84	91	98
105	112	119	126	133	140	147
154	161	168	175	182	189	196

How do you find multiples of 7?

Multiples of 7 by skip counting

Multiples of 7 by skip counting or repeated addition involve adding 7 to the numbers starting from 7. So, to show the first ten multiples of 7 by skip counting, we have,

Start: 7

7 + 7 = 14
14 + 7 = 21
21 + 7 = 28
28 + 7 = 35
35 + 7 = 42
42 + 7 = 49
49 + 7 = 56
56 + 7 = 63
63 + 7 = 70

Multiples of 7 by Multiplication

We find the multiples of 7 by multiplying seven by the counting numbers. Hence, we will multiply 7 by 1, 7 by 2, 7 by 3, and so on. The table below shows the first ten multiples of 7 by multiplying 7 by the first ten counting numbers.

1 × 7 = 7

2 × 7 = 14

3 × 7 = 21

4 × 7 = 28

5 × 7 = 35

6 × 7 = 42

7 × 7 = 49

8 × 7 = 56

9 × 7 = 63

10 × 7 = 70

Multiples of 7 by Division

Numbers that can be divided by seven precisely without any remainder are said to be multiples of seven.

Let us have the following examples:

( a ) 56 ÷ 7 = 8; since 56 can be divided by 7 without a remainder, it is a multiple of 7.
( b ) 77 ÷ 7 = 11; since 77 can be divided by 7 without a remainder, it is a multiple of 7.
( c ) 98 ÷ 7 = 14; since 98 can be divided by 7 without a remainder, it is a multiple of 7.
( d ) 105 ÷ 7 = 15; since 15 can be divided by 7 without a remainder, it is a multiple of 7.
( e ) 175 ÷ 7 = 25; since 175 can be divided by 7 without a remainder, it is a multiple of 7.

Multiples of 7 by a Simple Trick

Checking a number if it is a multiple of 7 involves these easy steps.

Step 1: Find twice the last digit of the given number.
Step 2: Subtract the answer in step 1 from the remaining digits.
Step 3: The given number is a multiple of 7 if the result in Step 2 is a multiple of 7.

Let us have the following numbers and check if they are multiples of 7:

( a ) 238 ( b ) 623 ( c ) 889 ( d ) 925

Solution

( a ) 238

To check if 238 is a multiple of 7, we must get twice 8 and subtract it from 23. If the difference is a multiple of 7, then 238 is a multiple of 7.

Twice of 8 = 16

23 – 16 = 7

Since 7 is a multiple of 7, the given number 238 is a multiple of 7.

( b ) 623

To check if 623 is a multiple of 7, we must get twice 3 and subtract it from 62. If the difference is a multiple of 7, then 623 is a multiple of 7.

Twice of 3 = 6

62 – 6 = 56

Since 56 is a multiple of 7, the given number 623 is a multiple of 7.

( d ) 889

To check if 889 is a multiple of 7, we must get twice nine and subtract it from 88. If the difference is a multiple of 7, then 889 is a multiple of 7.

Twice of 9 = 18

88 – 18 = 70

Since 70 is a multiple of 7, the given number 889 is a multiple of 7.

( 3 ) 925

To check if 925 is a multiple of 7, we must get twice 5 and subtract it from 92. If the difference is a multiple of 7, then 925 is a multiple of 7.

Twice of 5 = 10

92 – 10 = 82

Since 82 is not a multiple of 7, the given number 925 is not a multiple of 7.

Examples

Example 1

Calculate the sum or total of the first five multiples of 7.

Solution

The following are the first five multiples of 7:

7, 14, 21, 28, and 35.

Hence, we have,

Sum = 7 + 14 + 21 + 28 + 35

Sum = 105

Therefore, the sum or total of the first five multiples of 7 is 105.

Example 2

Calculate the sum or total of the multiples of 7 from 1 to 100.

Solution

The following are the multiples of 7 less than 100:

7	14	21	28	35	42	49
56	63	70	77	84	91	98

Sum ( multiples of 7 from 1 to 100 ) = 735

Sum = 735

Therefore, the sum or total of the multiples of 7 less than 100 is 735.

Example 3

List down the multiples of 7 that are less than 500.

Solution

There are 71 multiples of 7 that are less than 500. The table below shows the first 71 multiples of 7.

7	14	21	28	35	42	49	56	63	70
77	84	91	98	105	112	119	126	133	140
147	154	161	168	175	182	189	196	203	210
217	224	231	238	245	252	259	266	273	280
287	294	301	308	315	322	329	336	343	350
357	364	371	378	385	392	399	406	413	420
427	434	441	448	455	462	469	476	483	490
497

Example 4

Find the multiples of 7 from 100 to 1000.

Solution

One hundred twenty-eight (128) numbers are multiples of 7 from 100 to 1000. The table below shows these numbers.

105	112	119	126	133	140	147	154	161	168
175	182	189	196	203	210	217	224	231	238
245	252	259	266	273	280	287	294	301	308
315	322	329	336	343	350	357	364	371	378
385	392	399	406	413	420	427	434	441	448
455	462	469	476	483	490	497	504	511	518
525	532	539	546	553	560	567	574	581	588
595	602	609	616	623	630	637	644	651	658
665	672	679	686	693	700	707	714	721	728
735	742	749	756	763	770	777	784	791	798
805	812	819	826	833	840	847	854	861	868
875	882	889	896	903	910	917	924	931	938
945	952	959	966	973	980	987	994

Example 5

Solve the average of the first 20 multiples of 7.

Solution

The following are the first twenty multiples of 7:

7	14	21	28	35	42	49	56	63	70
77	84	91	98	105	112	119	126	133	140

To find the average, we must get the sum or total of these numbers and divide the answer by 20.

Sum of the first twenty multiples of 7 = 1470

Average = Sum / 20

Average = 1470 / 20

Average = 73.50

Therefore, the average of the first twenty multiples of 7 is 73.50.

Summary

Numbers that can be divided by seven precisely without any remainder are said to be multiples of seven. Let us say, for example, 56 is a multiple of seven since 56 ÷ 7 is 8.

The first few multiples of 7 are the answer to the seven times table.

Seven Times Table

1 × 7 = 7

2 × 7 = 14

3 × 7 = 21

4 × 7 = 28

5 × 7 = 35

6 × 7 = 42

7 × 7 = 49

8 × 7 = 56

9 × 7 = 63

10 × 7 = 70

11 × 7 = 77

12 × 7 = 84

13 × 7 = 91

14 × 7 = 98

15 × 7 = 105

There are infinite multiples of seven. Any number created by multiplying seven by natural or counting numbers is a multiple of 7. Since 0 × 7 = 0, 0 is also a multiple of 7.

Multiples of 7 up to 100

There are 14 multiples of 7 less than 100. These numbers include the following:

7	14	21	28	35	42	49
56	63	70	77	84	91	98

To find multiples of 7, we can use skip counting or repeated addition, multiplication, and division. There are also tricks to say whether a number is a multiple of 7.

Frequently Asked Questions on Multiples of 7 ( FAQs )

What is a multiple?

A multiple is a number resulting from multiplying one natural number or a counting number by another number.

So, for the multiples of seven, these numbers are obtained by multiplying 7 by the counting numbers. The table below shows multiplying 7 by the first ten natural numbers.

Seven Times Table

1 × 7 = 7

2 × 7 = 14

3 × 7 = 21

4 × 7 = 28

5 × 7 = 35

6 × 7 = 42

7 × 7 = 49

8 × 7 = 56

9 × 7 = 63

10 × 7 = 70

How do we determine whether a number is a multiple of 7?

Let us observe the list of multiples of 7 below:

These are multiples of 7 because dividing each number by seven will give us a remainder of zero. That is,

7 ÷ 7 = 1
14 ÷ 7 = 2
21 ÷ 7 = 3
28 ÷ 7 = 4
35 ÷ 7 = 5
42 ÷ 7 = 6
49 ÷ 7 = 7
56 ÷ 7 = 8
63 ÷ 7 = 9
70 ÷ 7 = 10

Thus, to say that a number is a multiple of 7, it should be in the form of 7n, where n is any counting or natural number.

How many numbers are multiples of seven?

There are infinite multiples of seven. Any number created by multiplying seven by natural or counting numbers is a multiple of 7.

Start counting from zero and keep adding 7 to find multiples of 7. To find the following multiple of 7, add 7 to the multiple you already know.

Are multiples of 7 odd numbers?

No. Not every multiple of 7 is odd.

Since there are numbers divisible by two and some are not, then the multiples of 7 have odd numbers or even.

What are the multiples of 7 starting from 1 up to 100?

Multiples of 7 up to 100

There are 14 multiples of 7 less than 100. These numbers include the following:

7	14	21	28	35	42	49
56	63	70	77	84	91	98

How to confirm if a number is a multiple of 7?

Numbers that can be divided by seven precisely without any remainder are said to be multiples of seven. Hence, a number must be divisible by 7 for it to be a multiple of seven.

Let us say, for example, 56 is a multiple of seven since 56 ÷ 7 is 8.

How many multiples of 7 are there, starting from 1 to 1000?

There are 142 multiples of 7 from 1 up to 1000. The table below shows the complete list.

7	14	21	28	35	42	49	56	63	70
77	84	91	98	105	112	119	126	133	140
147	154	161	168	175	182	189	196	203	210
217	224	231	238	245	252	259	266	273	280
287	294	301	308	315	322	329	336	343	350
357	364	371	378	385	392	399	406	413	420
427	434	441	448	455	462	469	476	483	490
497	504	511	518	525	532	539	546	553	560
567	574	581	588	595	602	609	616	623	630
637	644	651	658	665	672	679	686	693	700
707	714	721	728	735	742	749	756	763	770
777	784	791	798	805	812	819	826	833	840
847	854	861	868	875	882	889	896	903	910
917	924	931	938	945	952	959	966	973	980
987	994

Find the sum of the first ten multiples of 7.

We must add the first ten multiples of seven to get the sum.

Sum = 7 + 14 + 21 + 28 + 35 + 42 + 49 + 56 + 63 + 70

Sum = 385

Therefore, the sum of the first ten multiples of 7 is 385.

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