What are the Multiples of 42?
When the number 42 is multiplied by any natural number, the result is known as a multiple of 42. The multiple of 42 can be written as 42n where n can be any natural number. If we write the first n multiples of 42 that indicate we have to multiply 42 with the first n natural numbers.
For example: If we multiply 42 by 5, then the product is 210. As a result, we define 210 as a multiple of 42. Another thing to remember here is that the product of two numbers is a multiple of both the numbers. Hence, 210 is a multiple of 5 as well.
The multiples of 42 can be expressed in the form of 42 n, where n is a natural number.
And, n = 1, 2, 3, 4, 5, 6, …
The multiples of 42 will be:
42, 84, 126, 168, 210, 252, …
Thus, from the above observations, we can say that the multiples of 42 can be obtained by multiplying natural numbers with 42.
Also, we can observe that the difference between each succeeding number and the preceding number is 42, that is,
84 – 42 = 42,
126 – 84 = 42,
168 – 126 = 42, and so on.
For example: 294, 336 and 378 are all multiples of 42 because we can get these numbers mentioned here by multiplying 42 with some specific natural numbers.
42 x 7 = 294 | 42 multiplied by 7 to get 294 |
42 x 8 = 336 | 42 multiplied by 8 to get 336 |
42 x 9 = 378 | 42 multiplied by 9 to get 378 |
Finding Multiples of 42 by Repeated Addition?
Repeated addition indicates that we are adding a number to itself, in a repeated manner. We can also use repeated addition to find the multiples of a number.
If we want to find the first ten multiples of 42, we can write it in following way:
42 x 1 | 42 | |
42 x 2 | 42 + 42 | Here 42 added two times |
42 x 3 | 42 + 42 + 42 | Here 42 added three times |
42 x 4 | 42 + 42 + 42 + 42 | Here 42 added four times |
42 x 5 | 42 + 42 + 42 + 42 + 42 | Here 42 added five times |
42 x 6 | 42 + 42 + 42 + 42 + 42 + 42 | Here 42 added six times |
42 x 7 | 42 + 42 + 42 + 42 + 42 + 42 + 42 | Here 42 added seven times |
42 x 8 | 42 + 42 + 42 + 42 + 42 + 42 + 42 + 42 | Here 42 added eight times |
42 x 9 | 42 + 42 + 42 + 42 + 42 + 42 + 42 + 42 + 42 | Here 42 added nine times |
42 x 10 | 42 + 42 + 42 + 42 + 42 + 42 + 42 +42 + 42 + 42 | Here 42 added ten times |
The nth Multiple of 42
The nth multiple of 42 can be obtained by either multiplying 42 by n or by adding 42 n times;
nth multiple of 42 = 42 x n, or
nth multiple of 42 = 42 + 42 + ……… n times
[Note: n is any natural number.]
List of the First 10 Multiples of 42
42 x 1 | 42 |
42 x 2 | 84 |
42 x 3 | 126 |
42 x 4 | 168 |
42 x 5 | 210 |
42 x 6 | 252 |
42 x 7 | 294 |
42 x 8 | 336 |
42 x 9 | 378 |
42 x 10 | 420 |
Solved Multiples of 42 Examples
Example 1: Is 210 a multiple of 42?
Solution:
List multiples of 42.
42, 84, 126, 168, 210, 252,……
So, yes, 210 is a multiple of 42.
Example 2: What is the 12th multiple of 42?
Solution:
The 12th multiple of 42 can be obtained by the repeated addition of 42 for 12 times;
42 + 42 + 42 + 42 + 42 + 42 + 42 + 42 + 42 + 42 + 42 + 42 = 504
Hence, the 12th multiple of 42 is 504.
Example 3: Tom and John want to distribute food packets to the hungry and needy. Tom and John distributed 42 packets 5 and 7 times respectively. What will be the total number of food packets distributed?
Solution:
Tom and John distributed 42 packets 5 and 7 times respectively.
So, Tom and John distributed 42 x 5 = 210 and 42 x 7 = 294 respectively.
Total number of food packets distributed 210 + 294 = 504.
The multiples of a number are obtained by multiplying a number with a natural number.
If a number is multiplied with another number then the resultant product is known as a multiple, and the numbers being multiplied are known as factors of the resultant product.
For example : Forty two times three
The product 126 is a multiple of both 3 and 42.
The numbers 42 and 3 are the factors of 126.
The smallest multiple of 42 is 42 itself.
A number can be multiplied indefinitely so it can have an infinite number of multiples.