Explain the rules of divisibility, Mathematics

Assignment Help:

Explain the rules of Divisibility ?

Divisible by 2: If the last digit is a 0, 2, 4, 6, or 8, the number is evenly divisible by 2.

Divisible by 2

Not Divisible by 2

4, 12, 1006, 88, 100

5, 13, 1007, 89, 101

Divisible by 3: Add together the digits. If the result is evenly divisible by 3 (in other words, if the result is a multiple of 3), so is the original number.

Example 1: Is the number 2553 divisible by 3?

Step 1: Add the digits together.
(2 + 5 + 5 + 3) = 15

Step 2: Does 3 evenly divide into 15?
(15 / 3 ) = 5

The answer is yes. So 2553 is divisible by 3.

Example 2: Is the number 2554 divisible by 3?

Step 1: Add the digits together.
(2 + 5 + 5 + 4) = 16

Step 2: Does 3 evenly divide into 16?
(16/ 3) = 5 R 1

The answer is no. So 2553 is not divisible by 3.
Example 3: Is the number 4,715,448,735,448 divisibly by 3?

Step 1: Add the digits together.
(4 + 7 + 1 + 5 + 4 + 4 + 8 + 7 + 3 + 5 + 4 + 4 + 8) = 64

Now check to see if the number 64 is divisible by 3. 64 is still a pretty large number. If you do not want to go through the long-division process of dividing 64 by 3, you can keep adding the digits together until you get a number that is easier to work with.

Step 2: Add the digits together.
(6 + 4) = 10

Step 3: Does 3 evenly divide into 10?
(10 /3) = 3 R 1

The answer is no. So 64 is not divisible by 3; therefore, 4,715,448,735,448 is not divisible by 3.

Divisible by 4: Check to see if the number formed by the last two digits of the original number is divisible by 4.

Example: Is the number 291,583,791,283 divisible by 4?

Step 1: Check to see if 83 (the last two digits of the original number) is divisible by 4.
(83 / 4) = 20 R 3
The answer is no. So 291,583,791,283 is not divisible by 4.

Divisible by 5: If the last digit is a 0 or 5, the number is divisible by 5.

Divisible by 5

Not Divisible by 5

5, 10, 1005, 80, 100

4, 13, 1007, 89, 101


Divisible by 6: If the number is divisible by both 2 and 3, then it is divisible by 6.

Example: Is the number 186 divisible by 6?

Step 1: Check to see if 186 is divisible by 2.
Since the last digit is a 6, 186 is divisible by 2.
Step 2: Check to see if 186 is divisible by 3.
(1 + 8 + 6) = 15
(15 / 3) = 5
Since 15 is divisible by 3, 186 is divisible by 3.
Therefore, since 186 is divisible by both 2 and 3, then 186 is also divisible by the number 6.
Divisible by 9: Add together all the digits; if the result is divisible by 9, then so is the original number.

Example: Is the number 78,957 divisible by 9?

Step 1: Add the digits together.
(7 + 8 + 9 + 5 + 7) = 36
Now check to see if the number 36 is divisible by 9.

Step 2: Add the digits together.
(3 + 6) = 9
Since 9 evenly divides into 9, (9 / 9 =1), 36 is divisible by 9. Therefore, 78,957 is divisible by 9.
Divisible by 10: If the number ends in a 0, then it is divisible by 10.

Example: Which number, 12345 or 123450, is divisible by 10?
The answer is 123450, because it ends in a 0. 12345 is not divisible by 10, because it ends in 5.


Related Discussions:- Explain the rules of divisibility

Wronskian, In the earlier section we introduced the Wronskian to assist us ...

In the earlier section we introduced the Wronskian to assist us find out whether two solutions were a fundamental set of solutions. Under this section we will look at the other app

Can you explain slope, Can you explain slope and Slope is measured as rise/...

Can you explain slope and Slope is measured as rise/run?

Trinomial x2 + 2x + 1 what are the dimensions of the field, A farmer's rect...

A farmer's rectangular field has an area in which can be expressed as the trinomial x2 + 2x + 1. In terms of x, what are the dimensions of the field? Because the formula for th

Vectors, |a.x|=1 where x = i-2j+2k then calculate a

|a.x|=1 where x = i-2j+2k then calculate a

Prove complement of element in boolean algebra is unique, Prove that, the c...

Prove that, the complement of each element in a Boolean algebra B is unique.     Ans:  Proof: Let I and 0 are the unit and zero elements of B correspondingly. Suppose b and c b

Characteristics and limitations of moving average, Characteristics and Limi...

Characteristics and Limitations of moving average Characteristics of moving average 1) The more the number of periods in the moving average, the greater the smoothing

Find the third vertex of a triangle, Find the third vertex of a triangle if...

Find the third vertex of a triangle if its two vertices are (-1, 4) and (5, 2) and mid point of one side is (0, 3).

Good investment, Realtors estimate that 23% of homes purchased in 2004 were...

Realtors estimate that 23% of homes purchased in 2004 were considered investment properties. If a sample of 800 homes sold in 2004 is obtained what is the probability that at most

Evaluate following. 0ln (1+)excos(1-ex)dx substitution, Evaluate following....

Evaluate following. ∫ 0 ln (1 + π )   e x cos(1-e x )dx Solution The limits are little unusual in this case, however that will happen sometimes therefore don't get

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd