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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses interesting facts about diving whole numbers. By the end of the module students should be able to recognize a whole number that is divisible by 2, 3, 4, 5, 6, 8, 9, or 10.

Section overview

  • Division by 2, 3, 4, and 5
  • Division by 6, 8, 9, and 10

Quite often, we are able to determine if a whole number is divisible by another whole number just by observing some simple facts about the number. Some of these facts are listed in this section.

Division by 2, 3, 4, and 5

Division by 2

A whole number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8.

The numbers 80, 112, 64, 326, and 1,008 are all divisible by 2 since the last digit of each is 0, 2, 4, 6, or 8, respectively.

The numbers 85 and 731 are not divisible by 2.

Division by 3

A whole number is divisible by 3 if the sum of its digits is divisible by 3.

The number 432 is divisible by 3 since 4 + 3 + 2 = 9 size 12{4+5+2=9} {} and 9 is divisible by 3.

432 ÷ 3 = 144 size 12{"432" div 3="144"} {}

The number 25 is not divisible by 3 since 2 + 5 = 7 size 12{2+5=7} {} , and 7 is not divisible by 3.

Division by 4

A whole number is divisible by 4 if its last two digits form a number that is divisible by 4.
The number 31,048 is divisible by 4 since the last two digits, 4 and 8, form a number, 48, that is divisible by 4.
31048 ÷ 4 = 7262 size 12{"31048" div 4="7262"} {}
The number 137 is not divisible by 4 since 37 is not divisible by 4.

Division by 5

A whole number is divisible by 5 if its last digit is 0 or 5.

Sample set a

The numbers 65, 110, 8,030, and 16,955 are each divisible by 5 since the last digit of each is 0 or 5.

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Practice set a

State which of the following whole numbers are divisible by 2, 3, 4, or 5. A number may be divisible by more than one number.

Division by 6, 8, 9, 10

Division by 6

A number is divisible by 6 if it is divisible by both 2 and 3.
The number 234 is divisible by 2 since its last digit is 4. It is also divisible by 3 since 2 + 3 + 4 = 9 size 12{2+3+4=9} {} and 9 is divisible by 3. Therefore, 234 is divisible by 6.
The number 6,532 is not divisible by 6. Although its last digit is 2, making it divisible by 2, the sum of its digits, 6 + 5 + 3 + 2 = 16 size 12{6+5+3+2="16"} {} , and 16 is not divisible by 3.

Division by 8

A whole number is divisible by 8 if its last three digits form a number that is divisible by 8.
The number 4,000 is divisible by 8 since 000 is divisible by 8.
The number 13,128 is divisible by 8 since 128 is divisible by 8.
The number 1,170 is not divisible by 8 since 170 is not divisible by 8.

Division by 9

A whole number is divisible by 9 if the sum of its digits is divisible by 9.
The number 702 is divisible by 9 since 7 + 0 + 2 size 12{7+0+2} {} is divisible by 9.
The number 6588 is divisible by 9 since 6 + 5 + 8 + 8 = 27 size 12{6+5+8+8="27"} {} is divisible by 9.
The number 14,123 is not divisible by 9 since 1 + 4 + 1 + 2 + 3 = 11 size 12{1+4+1+2+3="11"} {} is not divisi­ble by 9.

Division by 10

A Whole number is divisible by 10 if its last digit is 0.

Sample set b

The numbers 30, 170, 16,240, and 865,000 are all divisible by 10.

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Practice set b

State which of the following whole numbers are divisible 6, 8, 9, or 10. Some numbers may be divisible by more than one number.

Exercises

For the following 30 problems, specify if the whole number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10. Write "none" if the number is not divisible by any digit other than 1. Some numbers may be divisible by more than one number.

Exercises for review

( [link] ) In the number 412, how many tens are there?

1

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( [link] ) Add 35, 16, and 7 in two different ways.

( 35 + 16 ) + 7 = 51 + 7 = 58 size 12{ \( "35"+"16" \) +7="51"+7="58"} {}
35 + ( 16 + 7 ) = 35 + 23 = 58 size 12{"35"+ \( "16"+7 \) ="35"+"23"="58"} {}

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( [link] ) Find the quotient 35 ÷ 0 size 12{"35" div 0} {} , if it exists.

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( [link] ) Find the quotient. 3654 ÷ 42 size 12{"3654" div "42"} {} .

87

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Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
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
what king of growth are you checking .?
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
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
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
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
7hours 36 min - 4hours 50 min
Tanis Reply

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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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