2.4 Find multiples and factors (Page 10/9)

Prealgebra Page 1 / 9

By the end of this section, you will be able to:

Identify multiples of numbers
Use common divisibility tests
Find all the factors of a number
Identify prime and composite numbers

Before you get started, take this readiness quiz.

Which of the following numbers are counting numbers (natural numbers)?
$0, 4, 215$
If you missed this problem, review Introduction to Whole Numbers .
Find the sum of $3, 5,$ and $7 .$
If you missed the problem, review Use the Language of Algebra .

Identify multiples of numbers

Annie is counting the shoes in her closet. The shoes are matched in pairs, so she doesn’t have to count each one. She counts by twos: $2, 4, 6, 8, 10, 12 .$ She has $12$ shoes in her closet.

The numbers $2, 4, 6, 8, 10, 12$ are called multiples of $2 .$ Multiples of $2$ can be written as the product of a counting number and $2 .$ The first six multiples of $2$ are given below.

\begin{array}{l} 1 \cdot 2 = 2 \\ 2 \cdot 2 = 4 \\ 3 \cdot 2 = 6 \\ 4 \cdot 2 = 8 \\ 5 \cdot 2 = 10 \\ 6 \cdot 2 = 12 \end{array}

A multiple of a number is the product of the number and a counting number. So a multiple of $3$ would be the product of a counting number and $3 .$ Below are the first six multiples of $3 .$

\begin{array}{l} 1 \cdot 3 = 3 \\ 2 \cdot 3 = 6 \\ 3 \cdot 3 = 9 \\ 4 \cdot 3 = 12 \\ 5 \cdot 3 = 15 \\ 6 \cdot 3 = 18 \end{array}

We can find the multiples of any number by continuing this process. [link] shows the multiples of $2$ through $9$ for the first twelve counting numbers.

Counting Number	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$
$Multiples of 2$	$2$	$4$	$6$	$8$	$10$	$12$	$14$	$16$	$18$	$20$	$22$	$24$
$Multiples of 3$	$3$	$6$	$9$	$12$	$15$	$18$	$21$	$24$	$27$	$30$	$33$	$36$
$Multiples of 4$	$4$	$8$	$12$	$16$	$20$	$24$	$28$	$32$	$36$	$40$	$44$	$48$
$Multiples of 5$	$5$	$10$	$15$	$20$	$25$	$30$	$35$	$40$	$45$	$50$	$55$	$60$
$Multiples of 6$	$6$	$12$	$18$	$24$	$30$	$36$	$42$	$48$	$54$	$60$	$66$	$72$
$Multiples of 7$	$7$	$14$	$21$	$28$	$35$	$42$	$49$	$56$	$63$	$70$	$77$	$84$
$Multiples of 8$	$8$	$16$	$24$	$32$	$40$	$48$	$56$	$64$	$72$	$80$	$88$	$96$
$Multiples of 9$	$9$	$18$	$27$	$36$	$45$	$54$	$63$	$72$	$81$	$90$	$99$	$108$

Multiple of a number

A number is a multiple of $n$ if it is the product of a counting number and $n .$

Recognizing the patterns for multiples of $2, 5, 10, and 3$ will be helpful to you as you continue in this course.

Doing the Manipulative Mathematics activity “Multiples” will help you develop a better understanding of multiples.

[link] shows the counting numbers from $1$ to $50 .$ Multiples of $2$ are highlighted. Do you notice a pattern?

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 2 are highlighted in blue. — Multiples of $2$ between $1$ and $50$

The last digit of each highlighted number in [link] is either $0, 2, 4, 6, or 8 .$ This is true for the product of $2$ and any counting number. So, to tell if any number is a multiple of $2$ look at the last digit. If it is $0, 2, 4, 6, or 8,$ then the number is a multiple of $2 .$

Determine whether each of the following is a multiple of $2 :$

ⓐ $489$
ⓑ $3,714$

Solution

ⓐ
Is 489 a multiple of 2?
Is the last digit 0, 2, 4, 6, or 8?	No.
	489 is not a multiple of 2.

ⓑ
Is 3,714 a multiple of 2?
Is the last digit 0, 2, 4, 6, or 8?	Yes.
	3,714 is a multiple of 2.

Got questions? Get instant answers now!

Determine whether each number is a multiple of $2 :$

ⓐ $678$
ⓑ $21,493$

ⓐ yes
ⓑ no

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Determine whether each number is a multiple of $2 :$

ⓐ $979$
ⓑ $17,780$

ⓐ no
ⓑ yes

Got questions? Get instant answers now!

Now let’s look at multiples of $5 .$ [link] highlights all of the multiples of $5$ between $1$ and $50 .$ What do you notice about the multiples of $5 ?$

All multiples of $5$ end with either $5$ or $0 .$ Just like we identify multiples of $2$ by looking at the last digit, we can identify multiples of $5$ by looking at the last digit.

Determine whether each of the following is a multiple of $5 :$

ⓐ $579$
ⓑ $880$

Solution

ⓐ
Is 579 a multiple of 5?
Is the last digit 5 or 0?	No.
	579 is not a multiple of 5.

ⓑ
Is 880 a multiple of 5?
Is the last digit 5 or 0?	Yes.
	880 is a multiple of 5.

Got questions? Get instant answers now!

Questions & Answers

what does the ideal gas law states

Joy Reply

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.

Kate Reply

To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.

Muhammed

What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?

Kate Reply

what is the change in momentum of a body?

Eunice Reply

what is a capacitor?

Raymond Reply

Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.

Gautam

A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate

Maria Reply

please solve

Sharon

8m/s²

Aishat

What is Thermodynamics

Muordit

velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.

Mehmet

A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat

Saheed Reply

50 m/s due south east

Someone

which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer

Ramon Reply

I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.

Someone

Scratch that

Someone

temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....

Someone

about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle

Someone

definitely of physics

Haryormhidey Reply

how many start and codon

Esrael Reply

what is field

Felix Reply

physics, biology and chemistry this is my Field

ALIYU

field is a region of space under the influence of some physical properties

Collete

what is ogarnic chemistry

WISDOM Reply

determine the slope giving that 3y+ 2x-14=0

WISDOM

Another formula for Acceleration

Belty Reply

a=v/t. a=f/m a

IHUMA

innocent

Adah

pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?

Nassze Reply

how do lnternal energy measures

Esrael

Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.

JALLAH Reply

No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.

Dlovan

Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?

Robert

like charges repel while unlike charges atttact

Raymond

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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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