To find the multiples of any number easily, it's important to understand what multiples are and how we get them.

A multiple of a number is what you get when you multiply that number by a whole number.

Let's take the number 5 as an example:

• 5 × 1 = 5
• 5 × 2 = 10
• 5 × 3 = 15
• 5 × 4 = 20
• 5 × 5 = 25

So, the multiples of 5 are {5, 10, 15, 20, 25, ...}.

How to Identify Multiples:

1. Using Basic Multiplication:

   • What is a Multiple?: A multiple of a number ( n ) is just ( n \times k ), where ( k ) is any whole number (like 0, 1, 2, 3, ...).
   • Example: For ( n = 3 ):
     • 3 × 0 = 0
     • 3 × 1 = 3
     • 3 × 2 = 6
     • 3 × 3 = 9
   • So, the multiples of 3 are: {0, 3, 6, 9, 12, ...}.

2. Looking for Patterns:

   • Multiples often follow patterns. For example:
     • The multiples of 2 are all the even numbers: {..., -4, -2, 0, 2, 4, 6, ...}.
     • The multiples of 5 always end in 0 or 5.
     • The multiples of 10 always end in 0.

3. Using Division to Check for Multiples:

   • To find out if a number ( x ) is a multiple of ( n ), divide ( x ) by ( n ):
   • If the result is a whole number, then ( x ) is a multiple of ( n ).
   • Example: Is 24 a multiple of 6?
     • When you calculate ( 24 ÷ 6 = 4 ), you get a whole number. So, yes, 24 is a multiple of 6.

How to Find Multiples Easily:

• Listing Method: Start from 0 and keep adding the number ( n ) until you reach the number you need.

• Skip Counting: Count by the number you want to find multiples of (for example, counting by 4s: 4, 8, 12, 16...).

Fun Facts About Multiples:

• Multiples can go on forever as you keep adding.
• Each number has an endless list of multiples. For instance, the multiples of 7 are {0, 7, 14, 21, ...} and they continue without end.

In summary, finding multiples of any number is simple! You use multiplication, notice patterns, and do some easy division to make sure you understand this basic math idea.