**Divisibility Hints**

How can division be simpler?

We are all looking to make things simpler on ourselves. When it comes to division there are a few simple rules that will make it easier to find what a number can be divided by.

How about them 2's

Can this number be divided by 2?

3's a charm!

Is the sum of the digits divisible by 3?

4 for four

5's around

Does the number end in either a 0 or a 5?

To see if a number can be divided by 2, follow this simple hint:

Is it an even number?

297

Since 297 is not even, then it cannot be divided by 2.

How about the number 182?

YES!

182 2 = 91

297

If is it, then YES, it can be divided by 2.

2+9+7=18

18 3=9

YES!

It is divisible by 3

297 3=99

2

97

If the two-digit numbers

97

4 = 24.25

No. 297 is not divisible by 4.

How about 9

28

?

28

4= 9 YES!

928 4= 232

in the tens and ones place is

divisible by 4.

297

297

297

297

297

182

928

29

7

does NOT end in a 0 or 5

How about 680?

YES! 68

0

ends in a

0

.

680 5= 136

680

Silly 6's

If the number is divisible by

2

AND by

3

612

Remember 297 was not divisible by 2 since it is not an even number, so it cannot be divided by 6.

The number 612 is even so it works for 2. Adding 6+1+2=9, so it can be divided by 3. YES! This works.

612 6= 102

Sorry 7's

Unfortunately there is no simple rule to see if a number is divisible by 7.

**Sorry!**

Enough 8's

This one is a little difficult.

Are the last three digits divisible by 8?

3160

297 8= 37.125

This does not divide evenly.

Try 3160

160 8= 20

Since 160 CAN be divided by 8... It works!

3160 8 = 395

Nothin' but 9's

The sum of all digits is divisible by 9.

This one may look similar to you.

2+9+7= 18

Why yes, 18 is divisible by 9.

297 9 = 33

Totally 10's

If the number ends in 0, it is divisible by 10.

Since 297 does not end in 0... it does NOT work.

543210

This ends on 0... so it WILL work

543210 10= 54321

543210

History of division

Division had been used for many years. When people were given food it needed to be divided up equally among those receiving.

Another way that division has been used for many year is when it comes to paying people. If you have a set number of people that do the work, a person would need to take the money earned from the job and divide it equally among the workers.

You would want your fair share,

Right!

Division Standards

SMP 5

Use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem.

References:

http://www.azed.gov/standards-practices/mathematics-standards-2/

It has been conjectured that Babylonian advances in mathematics were probably facilitated by the fact that 60 has many divisors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 - in fact, 60 is the smallest integer divisible by all integers from 1 to 6), and the continued modern-day usage of of 60 seconds in a minute, 60 minutes in an hour, and 360 (60 x 6) degrees in a circle, are all testaments to the ancient Babylonian system. It is for similar reasons that 12 (which has factors of 1, 2, 3, 4 and 6) has been such a popular multiple historically (e.g. 12 months, 12 inches, 12 pence, 2 x 12 hours, etc).

http://www.storyofmathematics.com/sumerian.html

https://www.khanacademy.org/math/pre-algebra/factors-multiples/divisibility_tests/v/divisibility-tests-for-2-3-4-5-6-9-10