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Determine whether each number is a multiple of 5 .

  1. 675
  2. 1,578

  1. yes
  2. no

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Determine whether each number is a multiple of 5 .

  1. 421
  2. 2,690

  1. no
  2. yes

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[link] highlights the multiples of 10 between 1 and 50 . All multiples of 10 all end with a zero.

The image shows a chart with five rows and ten columns. The first row lists the numbers from 1 to 10. The second row lists the numbers from 11 to 20. The third row lists the numbers from 21 to 30. The fourth row lists the numbers from 31 and 40. The fifth row lists the numbers from 41 to 50. All factors of 10 are highlighted in blue.
Multiples of 10 between 1 and 50

Determine whether each of the following is a multiple of 10 :

  1. 425
  2. 350

Solution

Is 425 a multiple of 10?
Is the last digit zero? No.
425 is not a multiple of 10.
Is 350 a multiple of 10?
Is the last digit zero? Yes.
350 is a multiple of 10.
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Determine whether each number is a multiple of 10 :

  1. 179
  2. 3,540

  1. no
  2. yes

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Determine whether each number is a multiple of 10 :

  1. 110
  2. 7,595

  1. yes
  2. no

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[link] highlights multiples of 3 . The pattern for multiples of 3 is not as obvious as the patterns for multiples of 2 , 5 , and 10 .

The image shows a chart with five rows and ten columns. The first row lists the numbers from 1 to 10. The second row lists the numbers from 11 to 20. The third row lists the numbers from 21 to 30. The fourth row lists the numbers from 31 and 40. The fifth row lists the numbers from 41 to 50. All factors of 3 are highlighted in blue.
Multiples of 3 between 1 and 50

Unlike the other patterns we’ve examined so far, this pattern does not involve the last digit. The pattern for multiples of 3 is based on the sum of the digits. If the sum of the digits of a number is a multiple of 3 , then the number itself is a multiple of 3 . See [link] .

Multiple of 3 3 6 9 12 15 18 21 24
Sum of digits 3 6 9 1 + 2 3 1 + 5 6 1 + 8 9 2 + 1 3 2 + 4 6

Consider the number 42 . The digits are 4 and 2 , and their sum is 4 + 2 = 6 . Since 6 is a multiple of 3 , we know that 42 is also a multiple of 3 .

Determine whether each of the given numbers is a multiple of 3 :

  1. 645
  2. 10,519

Solution

Is 645 a multiple of 3 ?

Find the sum of the digits. 6 + 4 + 5 = 15
Is 15 a multiple of 3? Yes.
If we're not sure, we could add its digits to find out. We can check it by dividing 645 by 3. 645 ÷ 3
The quotient is 215. 3 215 = 645

Is 10,519 a multiple of 3 ?

Find the sum of the digits. 1 + 0 + 5 + 1 + 9 = 16
Is 16 a multiple of 3? No.
So 10,519 is not a multiple of 3 either.. 645 ÷ 3
We can check this by dividing by 10,519 by 3. 3,506 R 1 3 10,519

When we divide 10,519 by 3 , we do not get a counting number, so 10,519 is not the product of a counting number and 3 . It is not a multiple of 3 .

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Determine whether each number is a multiple of 3 :

  1. 954
  2. 3,742

  1. yes
  2. no

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Determine whether each number is a multiple of 3 :

  1. 643
  2. 8,379

  1. no
  2. yes

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Look back at the charts where you highlighted the multiples of 2 , of 5 , and of 10 . Notice that the multiples of 10 are the numbers that are multiples of both 2 and 5 . That is because 10 = 2 5 . Likewise, since 6 = 2 3 , the multiples of 6 are the numbers that are multiples of both 2 and 3 .

Use common divisibility tests

Another way to say that 375 is a multiple of 5 is to say that 375 is divisible by 5 . In fact, 375 ÷ 5 is 75 , so 375 is 5 75 . Notice in [link] that 10,519 is not a multiple 3 . When we divided 10,519 by 3 we did not get a counting number, so 10,519 is not divisible by 3 .

Divisibility

If a number m is a multiple of n , then we say that m is divisible by n .

Since multiplication and division are inverse operations, the patterns of multiples that we found can be used as divisibility tests. [link] summarizes divisibility tests for some of the counting numbers between one and ten.

Divisibility Tests
A number is divisible by
2 if the last digit is 0 , 2 , 4 , 6 , or 8
3 if the sum of the digits is divisible by 3
5 if the last digit is 5 or 0
6 if divisible by both 2 and 3
10 if the last digit is 0

Determine whether 1,290 is divisible by 2 , 3 , 5 , and 10 .

Solution

[link] applies the divisibility tests to 1,290 . In the far right column, we check the results of the divisibility tests by seeing if the quotient is a whole number.

Divisible by…? Test Divisible? Check
2 Is last digit 0 , 2 , 4 , 6 , or 8 ? Yes. yes 1290 ÷ 2 = 645
3 Is sum of digits divisible by 3 ?
1 + 2 + 9 + 0 = 12 Yes.
yes 1290 ÷ 3 = 430
5 Is last digit is 5 or 0 ? Yes. yes 1290 ÷ 5 = 258
10 Is last digit 0 ? Yes. yes 1290 ÷ 10 = 129

Thus, 1,290 is divisible by 2 , 3 , 5 , and 10 .

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Questions & Answers

How we are making nano material?
LITNING Reply
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scanning tunneling microscope
Sahil
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
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Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
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Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
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what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
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what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
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absolutely yes
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how to know photocatalytic properties of tio2 nanoparticles...what to do now
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it is a goid question and i want to know the answer as well
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for teaching engĺish at school how nano technology help us
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How can I make nanorobot?
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Do somebody tell me a best nano engineering book for beginners?
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there is no specific books for beginners but there is book called principle of nanotechnology
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what is fullerene does it is used to make bukky balls
Devang Reply
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fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
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what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
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is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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Practice Key Terms 4

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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