What are the Multiples of 3?
Multiples are obtained when a number is multiplied by another number. Hence, the multiples of 3 are the results acquired when a natural number is multiplied by 3. For example, if we multiply 4 by 3, we get 12 which is a multiple of 3.
The general form of the multiples of 3 can be written as ‘3n’, where n is a natural number. We can find the different multiples of 3 by placing any natural number in the position of n.
When n = 1, 3n = 3
When n = 2, 3n = 6
When n = 3, 3n = 9
When n = 4, 3n = 12
The value of ‘n’ can go on till infinity. This indicates that 3 has an infinite number of multiples, just like any other number.
Times Table of 3
The multiples of 3 can be arranged in a table known as the times table of 3.
The times table of 3 can be extended up to any value of ‘n’.
Multiples of 3 on a Number line
The multiples of 3 can be represented on a number line as well. Have a look at the following number line:
Here, we can observe a pattern in the multiples of 3. There is a series of jumps such that 3 is added n number of times when we multiply 3 by n. So, the difference between any two successive multiples of 3 is 3.
Multiples of 3 through Repeated addition
A multiplication operation is essentially a simplified way to repeatedly add a number. So it is important to understand the concept of repeated addition.
In the given table multiples of 3 are obtained using repeated addition.
Here, we can see that we get the multiples of 3 by repeatedly adding 3. If 3 is added n times, we get the value of 3n, that is, the nth multiple of 3.
Since repeated addition is a time consuming method, using the times table of numbers is a better way to solve problems involving multiplication operations.
Solved Multiples of 3 Examples
Example 1: Is 22 a multiple of 3?
Answer: 22 is not a multiple of 3. The multiples of 3 closest to 22 are 21 and 24.
Example 2: Gary was arranging toys based on their size at the toy-shop. Once he finished with the arrangement, he noticed that the toys were arranged in a mathematical pattern. He had placed three toys on the first shelf. The second shelf had three more toys than the previous shelf and so on. How many toys do you think the 12th shelf has?
Answer: According to the problem, the first shelf has 3 toys. The second shelf has 3 more than the first shelf, that is, 6 toys. If you notice, these are multiples of 3.
So, we will multiply 3 by 12 to find the total number of toys on the 12th shelf, that is,
3 x 12 = 36
Hence, 36 toys were placed on the 12th shelf.
Example 3: What is the 14th multiple of 3?
Answer: In this problem, we can find the 14th multiple of 3 by using the ‘3n’ formula.
So, when n = 14, 3n = 3 \(\times\) 14 = 42
Thus, the 14th multiple of 3 is 42.
Example 4: Complete the pattern: 18, 21, 24, 27, _, 33, 36.
Answer:
If we observe the numbers here we can say that they are multiples of 3. So we can find the missing number by adding 3 to 27, that is,
27 + 3 = 30
Hence, the missing number in the pattern is 30.
The first five multiples of 3 are 3, 6, 9, 12, and 15.
The even multiples of 3 between 3 to 20 are 6, 12, and 18.
All numbers, including 3, have an infinite number of multiples.
The even multiples of 3 between 50 and 70 are 54, 60, and 66.
The divisibility rule for 3 is that a number is absolutely divisible by 3 if the sum of its digits is exactly divisible by 3.