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Understanding multiplication
Whole numbersEven numbers
Here you will learn about multiples, including how to calculate multiples of a number and solve problems using knowledge of multiples.
Students will first learn about multiples as part of operations and algebraic thinking in elementary school.
Multiples are the products you get when two numbers, or factors, are multiplied.
For example, the first five multiples of 7 are 7 , 14 , 21 , 28 , and 35 .
You can skip count on a number line to find multiples of 7 .
The number line shows the first 7 multiples of 7 , but you could keep skipping counting to find more multiples.
To make them easier to find, multiples of the numbers 1 to 9 have patterns. They can help you decide if a given number is a multiple of 1 to 9 .
Number | Multiples | Pattern |
---|---|---|
1 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10… | every number is a multiple of 1 |
2 | 2, 4, 6, 8, 10, 12, 14, 16, 18… | the last digit is an even number |
3 | 3, 6, 9, 12, 15, 18, 21, 24… | the sum of the digits is divisible by three |
4 | 4, 8, 12, 16, 20, 24, 28, 32… | the number is double of a multiple of \bf{2} |
5 | 5, 10, 15, 20, 25, 30, 35… | the last digit is zero or five |
6 | 6, 12, 18, 24, 30, 36, 42, 48… | the number is divisible by both two and three |
7 | 7, 14, 21, 28, 35, 42, 49, 56… | *No divisibility pattern |
8 | 8, 16, 24, 32, 40, 48, 56… | the number is double a multiple of \bf{4} |
9 | 9, 18, 27, 36, 45, 54, 63, 72… | the sum of the digits is divisible by nine |
10 | 10, 20, 30, 40, 50, 60… | the last digit is zero |
How does this relate to 4th grade math?
In order to find if a number is a multiple of another number:
Use this quiz to check your grade 4 to 6 students’ understanding of factors and multiples. 10+ questions with answers covering a range of 4th, 5th and 6th grade topics to identify areas of strength and support!
DOWNLOAD FREEUse this quiz to check your grade 4 to 6 students’ understanding of factors and multiples. 10+ questions with answers covering a range of 4th, 5th and 6th grade topics to identify areas of strength and support!
DOWNLOAD FREEIs 76 a multiple of 6 ?
Start a list of multiples for 6 :
6 , 12 , 18 , 24 , 30 …
Notice that the multiples of 6 are also multiples of 2 and 3 .
This pattern is true for all multiples of 6 .
2Decide if the number is a multiple.
✔ The last digit (6) is even, so it is a multiple of 2 .
✘ The sum of the digits (7 + 6 = 13) , so it is not a multiple of 3 .
76 is NOT a multiple of 6 because it is NOT a multiple of 3 .
Skip counting on a number line shows that 76 is NOT a multiple of 6 .
Is 65 a multiple of 5 ?
Think about the pattern for the multiples of the number.
Start a list of multiples for 5 :
5 , 10 , 15 , 20 , 25 …
Notice that they end in either a 5 or a 0 .
This pattern is true for all multiples of 5 .
Decide if the number is a multiple.
✔ 65 is a multiple of 5 because it ends in a 5 .
Skip counting on a number line shows that 65 is the 13^{th} multiple of 5 .
Is 66 a multiple of 4 ?
Think about the pattern for the multiples of the number.
Start a list of multiples for 4 :
4 , 8 , 12 , 16 , 20 …
Notice that they are all doubles of a multiple of 2 .
This pattern is true for all multiples of 4 .
Decide if the number is a multiple.
✘ 66 is the double of 33 \rightarrow 33 \times 2=66 , but 33 is not a multiple of 2 .
66 is not a multiple of 4 because it is not a double of a multiple of 2 .
Skip counting on a number line shows that 66 is NOT a multiple of 4 .
Is 72 a multiple of 9 ?
Think about the pattern for the multiples of the number.
Start a list of multiples for 9 :
9 , 18 , 27 , 36 , 45 …
Notice that the sum of the digits is divisible by 9 .
This pattern is true for all multiples of 9 .
Decide if the number is a multiple.
✔ 72 is a multiple of 9 , because the sum of the digits (7+2=9) is divisible by 9 .
Skip counting on a number line shows that 72 is the eighth multiple of 9 .
Is 42 a multiple of 3 ?
Think about the pattern for the multiples of the number.
Start a list of multiples for 3 :
3 , 6 , 9 , 12 , 15 …
Notice that the sum of the digits is divisible by 3 .
This pattern is true for all multiples of 3 .
Decide if the number is a multiple.
✔ 42 is a multiple of 3 , because the sum of the digits (4+2=6) is divisible by 3 .
Skip counting on a number line shows that 42 is the 14^{th} multiple of 3 .
An elementary school is performing a play. They want to put out 88 chairs for the audience. If they want the same amount of chairs in each row, should they do rows of 6 , 8 or 10 ?
Think about the pattern for the multiples of the number.
Multiples of 6 : the sum of the digits is divisible by three.
Multiples of 8 : the number is double a multiple of 4 .
Multiples of 10 : the last digit is zero.
Decide if the number is a multiple.
✘ 88 is NOT a multiple of 6 , because the sum of the digits (8 + 8 = 16) is NOT divisible by 3 .
✔ 88 is a multiple of 8 , because it is double a multiple of 4 \rightarrow 2 \times 44=88 .
The school should put the 88 chairs in rows of 8 .
1. Which number is a multiple of 2 ?
For multiples of 2 , the last digit is an even number. 54 ends in an even number and 27 \times 2=54 , so 54 is a multiple of 2 .
2. Which number is a multiple of 7 ?
Using a number line to skip count by 7 , shows that 91 is a multiple of 7 .
3. Which number is NOT a multiple of 3 ?
For multiples of 3 , the sum of the digits is divisble by three. 4+3=7 is not divisible by 3 , so 43 is NOT a multiple of 3 .
4. Which number is NOT a multiple of 4 ?
For multiples of 4 , the number is double a multiple of 2 . 58 is the double of 29 , so 58 is NOT a multiple of 4 .
5. A grocery store has 78 boxes of cereal. They want to put the same number of boxes on each shelf. How many boxes should they put on each shelf?
4 boxes
5 boxes
6 boxes
7 boxes
For multiples of 6 , the number is divisible by both two and three. 78 is a multiple of 2 , because it ends in an even number (8) .
78 is a multiple of 3 , because 7 + 8 = 15 and 15 \div 3 = 5 .
So 78 is a multiple of 6 \rightarrow 6 \times 13=78
The grocery store can put 6 boxes on each shelf.
Times tables are a list of multiplication equations for a certain number and include both factors and multiples. Multiples are the answers (products) in times tables.
Yes, if a number divides another number without a remainder, it’s a multiple. For example, in the question “is 72 a multiple of 2 ?” you can solve 72 \div 2=36 . There are no remainders, so it is a multiple.
All positive and negative numbers have multiples. However, in 4th grade math you only work with positive numbers.
Prime numbers have an infinite amount of multiples but only 2 factors.
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