Class 5 - Multiples

Multiples are an important idea in math class. Factors and multiples help us find patterns in numbers, make fractions for bigger or smaller numbers.

Table of Contents

• What are Multiples?
• List of Multiples
• Properties of Multiples
• Difference Between Factors and Multiples
• Solved Problems on Multiples
• Practice Questions on Multiples

What are Multiples?

When you multiply a number by 1, 2, 3, 4, and so on, the results you get are called the multiples of that number.

Think of it like skip counting. If you skip count by 3 3, 6, 9, 12, 15 every number you land on is a multiple of 3. A multiple of a number is basically what you get when that number is repeated in addition or multiplied by a whole number.

For example, if you take the number 3 and multiply it step by step:

Example	Multiplication	4 × 1	4 × 2	4 × 3	4 × 4	4 × 5	4 × 6	4 × 7	4 × 8
Find multiples of 4	Multiples of 4	4	8	12	16	20	24	28	32

So 4, 8, 12, 16, and 20 are all multiples of 4. You can keep going as far as you like the list of multiples for any number never really ends.

Example	Multiplication	9 × 1	9 × 2	9 × 3	9 × 4	9 × 5	9 × 6	9 × 7	9 × 8
Find multiples of 9	Multiples of 9	9	18	27	36	45	54	63	72

A multiple of a number is always greater than or equal to the number itself (as long as you multiply by a whole number that is 1 or more).

List of Multiples

A number can have infinitely many multiples since multiples of a number are obtained by multiplying it by natural numbers. Thus, we can write an infinite number of multiples for a given number. The table below shows the first 10 multiples of a few numbers.

Number	First 10 Multiples
2	2, 4, 6, 8, 10, 12, 14, 16, 18, 20
3	3, 6, 9, 12, 15, 18, 21, 24, 27, 30
4	4, 8, 12, 16, 20, 24, 28, 32, 36, 40
5	5, 10, 15, 20, 25, 30, 35, 40, 45, 50
6	6, 12, 18, 24, 30, 36, 42, 48, 54, 60
7	7, 14, 21, 28, 35, 42, 49, 56, 63, 70
8	8, 16, 24, 32, 40, 48, 56, 64, 72, 80
9	9, 18, 27, 36, 45, 54, 63, 72, 81, 90
10	10, 20, 30, 40, 50, 60, 70, 80, 90, 100

Some numbers appear in more than one row for example, 12 appears in the multiples of 2, 3, 4, and 6. These are called common multiples and they become very useful when you work with topics like LCM (Lowest Common Multiple).

Properties of Multiples

Understanding the basic rules of multiples saves a lot of time when solving problems. Here are the key properties to remembering:

• Every number is a multiple of itself. For example, 7 is a multiple of 7 because 7 × 1 = 7.
• Every number is also a multiple of 1. This is because any number multiplied by 1 gives the number itself.
• Zero is a multiple of every number. Since any number multiplied by 0 gives 0, zero technically qualifies as a multiple of all numbers. However, in most school problems, multiples are listed starting from the number itself (i.e., multiplying from 1 onwards).
• The multiples of a number go on without end. No matter how large a number gets, you can always find one more multiple by multiplying by the next whole number. This is why we say multiples form an infinite list.
• A multiple of a number is always greater than or equal to that number (when you multiply by natural numbers starting from 1).
• Every multiple of a number can be divided by that number without leaving a remainder. For example, 30 is a multiple of 5 because 30 ÷ 5 = 6, with nothing left over.

Difference Between Factors and Multiples

Students often mix up factors and multiples because both relate to multiplication and division. Here is a clear side-by-side comparison to set things straight:

Point of Difference	Factors	Multiples
What it means	A number that divides another number completely	A number obtained by multiplying the given number by a whole number
Size compared to the number	Always less than or equal to the number	Always greater than or equal to the number
Is the list finite or infinite?	Finite (limited)	Infinite (never-ending)
How to find them	Use division	Use multiplication
Example (for number 6)	Factors of 6 are 1, 2, 3, 6	Multiples of 6 are 6, 12, 18, 24, 30…

A simple way to remember the difference: factors go below, multiples go above. Factors are smaller (or equal) and multiples are larger (or equal) compared to the original number. if A divides B completely, then A is a factor of B, and B is a multiple of A. They are two sides of the same relationship.

For example, since 4 × 5 = 20: 4 and 5 are factors of 20. 20 is a multiple of both 4 and 5.

Solved Problems on Multiples

Problem 1: Write the first five multiples of 9.

Multiply 9 by 1, 2, 3, 4, and 5:

9 × 1 = 9 9 × 2 = 18 9 × 3 = 27 9 × 4 = 36 9 × 5 = 45

The first five multiples of 9 are 9, 18, 27, 36, and 45.

Problem 2: Is 56 a multiple of 8?

Divide 56 by 8: 56 ÷ 8 = 7. There is no remainder.

Yes, 56 is a multiple of 8. (Because 8 × 7 = 56.)

Problem 3: Find the common multiples of 4 and 6 up to 50.

Multiples of 4 up to 50: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48 Multiples of 6 up to 50: 6, 12, 18, 24, 30, 36, 42, 48

Numbers that appear in both lists: 12, 24, 36, 48.

These are the common multiples of 4 and 6 up to 50.

Problem 4: A baker bakes bread in batches of 6. How many loaves will he have after 7 batches?

This is simply finding a multiple: 6 × 7 = 42 loaves.

Problem 5: Write the first four common multiples of 3 and 5.

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60… Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60…

Common multiples: 15, 30, 45, 60.

Practice Questions on Multiples

1. Write the first six multiples of 11.
2. Is 72 a multiple of 9? Show your working.
3. Find all the common multiples of 5 and 8 that are less than 100.
4. A school bus can seat 12 students per trip. How many students can be transported in 5 trips?
5. Which number among 42, 45, 48, and 50 is a multiple of both 6 and 8?
6. Write the first five multiples of 15.
7. Find the smallest common multiple of 4, 6, and 10.
8. True or false: Every even number is a multiple of 2. Explain your answer.
9. List three multiples of 13 that are greater than 100.
10. A shop packs apples in boxes of 8. If they have 200 apples, is 200 a multiple of 8? Can all apples be packed without any leftover?