What are the Multiples of 7?
The multiples of 7 are the products obtained by multiplying 7 by natural numbers. For example, we get 35 when we multiply 7 by 5. That means 35 is a multiple of 7. Similarly, 7, 14, 21, 28 and so on are the multiples of 7.
The general form of the multiples of 7 can be written as 7n, where n is a natural number. We can find the different multiples of 7 by placing any natural number in the position of n.
When n = 1, 7n = 7
When n = 2, 7n = 14
When n = 3, 7n = 21
When n = 4, 7n = 28
The value of n can go on till infinity. That means 7 has an infinite number of multiples, just like any other number. We can observe a pattern among the multiples of 7 with the help of a number line.
Here, we can notice that the multiples of 7 are essentially a series of jumps on the number line. In other words, we are adding 7 n number of times when we multiply 7 by n. So, the difference between any two successive multiples of 7 is 7.
Times Table of 7
The multiples of 7 can be arranged in a table known as the times table of 7.
The times table of 7 can be extended up to any value of n.
Finding the Multiples of 7 by Repeated Addition
Multiplication is an operation used for simplifying repeated addition. Memorizing the times table of numbers helps us quickly solve math problems involving repeated addition. However, to understand multiplication, we need to learn the idea of repeated addition.
Here, we can see that we get the multiples of 7 by repeatedly adding 7. If 7 is added n times, we get the value of 7n, that is, the nth multiple of 7.
Multiples and Factors of 7
As we have already learned, the multiples of 7 are the numbers obtained by multiplying 7 by any natural number. On the other hand, the factors of 7 are the numbers that can be multiplied with other numbers to give the 7 as the product. In the case of 7, the factors are 1 and 7.
According to the relationship between multiples and fractions, we can say that 7 is a multiple of 1 and 7. So, the numbers that are multiplied to obtain a multiple are known as the factors of the multiple.
Solved Multiples of 7 Examples
Example 1: Is 37 a multiple of 7?
Solution: 37 is not a multiple of 7. The multiples of 7 closest to 37 are 35 and 42.
Example 2: What is the 11th multiple of 7?
Solution: The 11th multiple of 7 can be calculated by multiplying 7 by 11.
7 x 11 = 77
Hence, the 11th multiple of 7 is 77.
Example 3: Complete the pattern: 84, 91, 98, 105, ___, 119, 126.
Solution: The numbers provided in the list are the multiples of 7.
We can find the missing number by calculating 105 + 7. So, the missing number is 112.
The list becomes 84, 91, 98, 105, 112, 119, 126.
Example 4: Gregor and Ellie gave a total of 28 chocolates to their children. If each child got 7 chocolates, find the number of children in their family.
Solution: Since we know that there are a total of 28 chocolates and each child got 7 chocolates, we can find the number of children in the family. We just need to find the number by which 7 is multiplied to obtain 28.
7 x n = 28
Where n is the number of children in the family.
So, n = 4
Hence, there are 4 children in the family.
Example 5: There are 12 students in a class. If the school decides to give each student 7 notebooks, how many notebooks should they purchase?
Solution:
Total number of students in the class = 12
Number of books distributed to each student = 7
Total number of books required = 12 x 7 = 84
So, the school needs to purchase 84 notebooks.
Multiples are numbers obtained by multiplying two numbers. For example, the multiples of 2 are 2, 4, 6, 8, 10 and so on.
All numbers, including 7, have an infinite number of multiples.
The first ten positive multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63 and 70.
The multiples of 7 between 70 and 100 are 77, 84, 91 and 98.
The 7th multiple of 7 is 49.
[Note: Since 7 is multiplied by itself to get 49, the number 49 is known as the square of 7.]