What are the Multiples of 14?
Every multiple of 14 is the product obtained by multiplying 14 by any natural number. For example, we get 28 when we multiply 14 by 2. That means 28 is a multiple of 14. Similarly, 14, 28, 42, 56, 70 and so on are the multiples of 14.
The general form of the multiples of 14 can be written as 14n, where n is a natural number. We can find the different multiples of 14 by substituting any natural number in the position of n.
When n = 1, 14n = 14
When n = 2, 14n = 28
When n = 3, 14n = 42
When n = 4, 14n = 56
The value of n can go on till infinity. This shows us that 14 has an infinite number of multiples, just like any other number.
Times Table of 14
The multiples of 14 can be arranged in a table known as the times table of 14.
As shown in the image, the times table of 14 can be extended up to any value of n.
Finding the Multiples of 14 by Repeated Addition
Multiplication is an operation used to simplify repeated addition. Memorizing the times table of numbers helps us quickly solve math problems involving repeated addition. However, to understand multiplication, we need to first learn the idea of repeated addition.
Multiplication table of 14 | Repeated addition of 14 | Explanation |
|---|---|---|
14 x 1 = 14 | ||
14 x 2 = 28 | 14 + 14 = 28 | Here 14 is added twice |
14 x 3 = 42 | 14 + 14 + 14 = 42 | Here 14 is added thrice |
14 x 4 = 56 | 14 + 14 + 14 + 14 = 56 | Here 14 is added four times |
14 x 5 = 70 | 14 + 14 + 14 + 14 + 14 = 70 | Here 14 is added five times |
14 x 6 = 84 | 14 + 14 + 14 + 14 + 14 + 14 = 84 | Here 14 is added six times |
Here, we can see that we get the multiples of 14 by repeatedly adding 14. If 14 is added n times, we get the value of 14n, that is, the nth multiple of 14.
Pattern in the Multiples of 14
We can also observe a pattern among the multiples of 14 with the help of a number line.
We can notice that the multiples of 14 are essentially a series of jumps on the number line, and the jump in this case lands on a multiple of 14.
In other words, we are adding 14 ‘n’ times when we multiply 14 by n. So, the difference between any two successive multiples of 14 is 14.
Rapid Recall
Solved Multiples of 14 Examples
Example 1:
List the common multiples of 14 and 21.
Solution:
The multiples of 14 include: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, 224, 238, 252, 266, 280, 294, 308, 322, 336, 350….
The multiples of 21 are: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, 315, 336, 357, 378, 399, 420….
Thus, the common multiples of 14 and 21 are 42, 84, 126, 168, 210, 252, 294, 336, and so on.
Example 2:
What are the multiples of 14 up to 100?
Solution:
The multiples of 14 up to 100 are 14, 28, 42, 56, 70, 84, and 98.
These can be written as:
14 × 1 = 14
14 × 2 = 28
14 × 3 = 42
14 × 4 = 56
14 × 5 = 70
14 × 6 = 84
14 × 7 = 98
Example 3:
Cindy was hosting a party for her friends. She wants to give each of her friends 5 chocolates in a goodie-bag when they return home. How many chocolates would she need in total if she has a total of 14 friends?
Solution:
Cindy wants to give 5 chocolates to each of her friends.
Cindy has 14 friends in total.
She will therefore require 14 times 5, that is, 14 x 5 = 60 chocolates in total.
The first ten multiples of 14 are: 14, 28, 42, 56, 70, 84, 98, 112, 126, and 140 are the first 10 multiples of 14.
If we can write a number in the form 14 times n, where n is a natural number, then that number is a multiple of 14. By multiplying numbers like 1, 2, 3, 4, 5 and so on by 14, we can get the multiples of 14.
For instance,
14 × 1 = 14
14 × 2 = 28
14 × 3 = 42
The multiples of 14 in this example are 14, 28, 42, and so on.
Factors of 14 are natural numbers that can evenly divide 14, that is, leave no remainder.
56, 70, 84, and 98 are the multiples of 14 between 50 and 100.