What is a Multiple?
A multiple can be defined as a number obtained by multiplying a number by an integer.
The multiples of a whole number are obtained by calculating the product of any of the counting numbers and that of the whole numbers.
For example, to find the multiples of the number 7, we will multiply 7 by 1, 7 by 2, 7 by 3, etc. The multiples are the product of this multiplication. Any number that can be represented as in the form of 7n, where n is considered as an integer and a multiple of 9.
Any number in Mathematics is a multiple of itself (Number x 1 = Number).
Any number in maths is a multiple of 1 (1 x Number = Number).
Zero is always multiple of every number (0 x number = 0).
What is a Common Multiple?
A common multiple is defined as a number that is a multiple of two or more numbers in a given set. Let us understand through an example.
Let us take two numbers 9 and 27
The common multiples of 9 are 9,18,27,36,45,54,63,81
The common multiples of 27 are 27,54,81
Here, we can see 9 and 27 have common multiples like 27,54 and 81
So to find the multiples of the number 7, simply multiply this number by a number of the set of natural numbers as many times as we want. See below how to do this for the number 7, let’s find the multiples of 7.
7 x 0 = 0 so we can say 0 is a multiple of 7.
7 x 1 = 7 so we can say that 7 is a multiple of 7.
7 x 2 = 14 so we can say that 14 is a multiple of 7.
7 x 3 = 21 so we can say that 21 is a multiple of 7.
7 x 4 = 28 so we can say that 28 is a multiple of 7.
How to Find Multiples Using Multiplication?
We can find multiples by multiplying the number with any integer.
Examples Showing the Multiples of 7 Multiply 7 by 1, then by 2, then by 3, then by 4 and so on. 7*1= 7, 7*2 =14, 7*3 =21, 7*4 =28, 7*5= 35,7*6=42 Hence, the first 6 multiples of 7 are 7, 14, 21, 28, 35, 42 |
How to Find Multiple Using Division?
As we know, both multiplication and division are inverse operations. It implies both are linked with each other. We can find out using division whether a given number is multiple of another number or not.
Some of the examples are mentioned below:
21÷ 7 = 3, so 21 can be divided evenly by 7 and is also a multiple of 7. Since, 3 * 7= 21.
49÷ 7 = 7, so 49 can be divided by 7 and is also a multiple of 7. Since, 7 * 7= 49
7 | 14 | 21 | 28 | 35 |
All the numbers that can be easily divided by the number 7 or a product of 7 are considered as the multiple of 7. The multiple is also known as factors and it relies on their usage in the equation also.
What is a Multiple of 7?
Any number that can be represented as in the form of 7n , where n is considered as an integer and a multiple of 7. So, if two values x and y are there, we can say that y is a multiple of x if y = nx for some integer n.
70 | = | 7 | x | 10 |
84 | = | 7 | x | 12 |
91 | = | 7 | x | 13 |
700 | = | 7 | x | 100 |
These values are known as multiple as we received these values by adding and subtracting the original value several times.
Multiplication | Multiples of 7 |
7 * 1 | 7 |
7 * 2 | 14 |
7 * 3 | 21 |
7 * 4 | 28 |
7 * 5 | 35 |
7 * 6 | 42 |
7 * 7 | 49 |
7 * 8 | 56 |
7 * 9 | 63 |
7 * 10 | 70 |
Solved Examples-
Question 1. Write any 5 Multiples of the Number 9.
Ans. Here are the five multiples of 9 - 9,18,27,36,45
Question 2. Write any 6 Multiples of Each of the Following:
1. 15
2. 12
Ans.
1. The six multiples of 15 are- 15,30,45,60,75,90
2. The six multiples of 12 are- 12,24,36,48,60,72
Q1. Can Factors, Division, Integers are Negative Numbers be Multiple?
Ans. Multiple of a number is defined as a number that is received by multiplying the given number with another integer.
All the numbers have multiples, if they can be multiplied by any number, they include their own times’ table. Also where there are multiples, there is a factor because each integer is considered as both a factor and multiple of itself.
Yes, factors, division, integers, and negative numbers can be considered as the multiples of a number because it is the most important Mathematical operation after addition and subtraction.
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