Multiples of 4

Did you know that 4 is the only number that is equal to the number of letters in its name? In this mini-lesson, we will discuss about the multiples of 4 and learn interesting facts about these multiples.

• First five multiples of 4: 4, 8, 12, 16, 20
• Prime factorization of 4: 4 = 2 × 2 = 2²

To get the multiples of a number, we need to multiply natural numbers with integers. A multiple is a product of a number with another number. If X is a multiple of a and b, it means a × b = X. Here a and b are natural numbers and X is the resultant multiple. Below are few examples to justify the above definition mathematically. For example, 4 × 9 = 36. 36 is a multiple of 9 and 4.

Now consider

• 4 × 1 = 4
• 4 × 2 = 8 
• 4 × 3 = 12
• 4 × 4 = 16

Look at the number line below and observe the pattern showing multiples of 4.

In the number line above, do you observe that the multiples of 4 have a pattern of addition hidden? Yes, you just learned another method to find multiples, i.e., addition of a number to itself. According to this, the first five multiples you just learned are 4, 8, 12, 16, and 20.

Important Notes:

• Here is a list of the most important and useful identities.

1. The first multiple of every number is the number itself, 4 × 1 = 4 
2. The multiples of a number are an infinite chain.
   4 × 1 = 4
   4 × 2 = 8
   4 × 3 = 12
   4 × 4 = 16 and so on
3. Every multiple of a number is greater than or equal to the number itself.
   4 × 1 = 4 (4=4)
   4 × 2 = 8, (8>4) 
   4 × 3 = 12,(12>4)
   4 × 4 =16,(16>4) and so on
4. Multiples of an even number are always even.

5. A multiple is termed to be a common multiple if it is common to two or more numbers.
   Example:
   9 × 2 = 18
   2 × 9 = 18

18 is a common multiple of 9 and 2.

In the above section, you have learned about the first 5 multiples of 4. In this section, you will be finding the next 15 multiples of 4

Please use a number line.

Hurray! In the end, you have a total of 20 multiples of 4. If you separate the alternate numbers after 8, that is 16, 24, 32, etc. each one of them is a multiple of 8.

To understand the concept of finding multiples, let us take a few more examples.

• Multiples of 5 - The first five multiples of 5 are 5, 10, 15, 20, 25
• Multiples of 6 - The first five multiples of 6 are 6, 12, 18, 24, 30
• Multiples of 7 - The first five multiples of 7 are 7, 14, 21, 28, 35
• Multiples of 8 - The first five multiples of 8 are 8, 16, 24, 32, 40
• Multiples of 9 - The first five multiples of 9 are 9, 18, 27, 36, 45

Challenging Questions:

• Can you find the multiples of 4, multiples of 9, and multiples of 15? Can you find their factors as well?

What are the common multiples of 3 and 4?

Common multiples of 3 and 4 are infinite. 
They are 12, 24, 36, and so on.

What are the 5 multiples of 4?

There are infinite multiples of 4. The first 5 multiples of 4 are:

• 4 × 1 = 4
• 4 × 2 = 8
• 4 × 3 = 12
• 4 × 4 = 16
• 4 × 5 = 20

Are the multiples of 4 always even?

Yes. We know that 4 is an even number and multiples of an even number are always even.

What is the least common multiple of 4 and 6?

The least common multiples of two numbers 4 and 6 can be calculated using the formula: product of the numbers/GCF of the numbers where GCF(4, 6) is the greatest common factor of 4 and 6.

GCF(4, 6) = 2
LCM(4, 6) = (4 × 6)/GCF(4, 6) = 24/2 = 12

Is 2 a multiple of 4?

No, 2 is not a multiple of 4.