All Multiples of 18
In mathematics, multiple is considered as the product of any quantity with an integer. In simpler words, if there are two quantities x and y, we can say that x is the multiple of y if x = ny for some integer n. Here, n is termed as the multiplier. If x is not zero, then it will be equivalent to say that x/y is an integer. The basics and concepts of this Multiples chapter are taught in school. It is necessary to be clear with this chapter for understanding the other advanced chapters of mathematics and physics. In this article, we will learn about the multiples of the factor of 18.
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Overview on Multiples of 18
Multiples of 18 are the numbers that can get divided by 18. These multiples don't leave any remainder when they are divided by 18. The quotient of this multiples, when divided by 18, is always a natural number. List of 18 multiples is infinite and has no limit. Let's list out some of the multiples to give an overview:
18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252,.........
Many students have the misconception that factors are also multiples, but that is wrong. Students thinking this is not clear on the concepts of multiples as well as factors. Factors of 18 are those numbers which are multiplied together in order to obtain the original number which is 18. Whereas, multiples are the term that is given to the numbers that can be written in the form of np, where n is considered as the series of natural numbers and p is considered as the number of which we need to obtain the multiples.
Another important thing to remember regarding multiples is that when the multiples of a number get divided by the original number, then the result obtained comes out to be a whole number. Let us see some examples:
Let's take three multiples of 18 - 18, 36, 54
When these three multiples are divided by 18, which is the original number, the results are:
18 ÷ 18 = 1
36 ÷ 18 = 2
54 ÷ 18 = 3
Here 1, 2 and 3 are whole numbers.
What do You Understand by Multiples of 18?
Any number that can be denoted in the form of 18n where n is any natural number or an integer, then that number is considered as a multiple of 18. To give a detailed view, numbers such as 18, 36, 54, 180, 360, 540 are Multiple of 18. The justification is given in the table below:
Justification for Multiples of 18
The values that are obtained are termed as 18 Multiples because these values are coming out by adding and subtracting the original value many times.
To give a cleared view on this chapter and all Multiple of 18, here are the first 20 Multiples of 18 Chart:
Multiples of 18 Chart
How to Find the 9th Multiple of 18?
In order to find the 9th Multiple of 18, a student needs to multiply 18 with 9, which is the required number as we are aiming to obtain the 9th Multiple of 18. In this case, n is considered as 9.
18 × n = 18n
18 × 9 = 162
Therefore, the 9th Multiple of 18 is 162
Suppose a student needs to find the 4th Multiple of 18.
18 × 4 = 72.
Likewise, every Multiple of 18 can be obtained using this formula.
Fun Facts
Zero is considered as the Multiple of every number because when any number is multiplied with zero, the product obtained is also zero. So be it a bigger number or a smaller number, every number has one common multiple which is zero.
Solved Problems
1. What is the 3rd Multiple of 18?
Solution:
Let consider n as 3 because we are finding out the 3rd multiple
18 × n = 18n
18 × 3 = 54
Therefore the 3rd Multiple of 18 is 54
2. What is the 6th Multiple of 18?
Solution:
First case:
Let's consider n as 6 because we are finding out the 6th multiple.
18 × n = 18n
18 × 6 = 108
Therefore the 6th Multiple is 108.
Q1. What are the Factors?
Answer: If a number is considered as a factor of any other (second) number, then it is mandatory that the first number should completely divide the second number without leaving any remainder and the quotient will be a natural number. In simple words, if a number which is considered as a dividend is exactly divisible by any other number which is considered as a divisor, then the divisor is deemed to be the factor of that dividend. Every number has a common factor which is one and the number itself. For example, 4 is a factor of 24, exactly giving 6 as quotient and leaving zero as remainder.
Q2. What are the Differences Between Factors and Multiples?
Answer: The difference between factors and multiples are:
S. no | Factors | Multiples |
1 | Factors are termed as the exact divisors of certain numbers. | The multiples are termed as the numbers which are obtained when it is multiplied with other numbers. |
2 | The number of factors of a number is finite. | The number of multiples of a number is infinite. |
3 | The operation that is used for finding out factors is division. | The operation that is used for finding out multiples is multiplication. |
4 | The result of the factors are less than or equal to the given number. | The result of the factors is higher than or equal to the given number. |