**Practice Questions on Divisibility Rules :**

In this section, we will see some practice questions on divisibility rules.

**Question 1 :**

If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be ?

(A) 2 (B) 3 (C) 4 (D) 5

**Solution :**

**Divisibility rule for 3 :**

If the sum of all the digits of the given number is divisible by 3, then we decide that the given number is also divisible by 3.

Let "x" be the unknown, then

= (5 + 1 + 7 + x + 3 + 2 + 4) / 3

= (22 + x) / 3

If x = 2, then 22 + x will become 24 and it is divisible by 3.

Hence the smallest whole number for x should be 3.

**Question 2 :**

If the number 481*673 is completely divisible by 9, then the smallest whole number in the place of * will be ?

(A) 4 (B) 3 (C) 6 (D) 7

**Solution :**

**Divisibility rule for 9 :**

If the sum of all the digits of the given number is divisible by 9, then we decide that the given number is also divisible by 9.

= (4 + 8 + 1 + x + 6 + 7 + 3) / 9

= (29 + x) / 9

If x = 1, then = (29 + 1) / 9 = 30/9 Not divisible by 9 |
If x = 4, then = (29 + 4) / 9 = 33/9 Not divisible by 9 |

If x = 7, then

= (29 + 7) / 9

= 36/9

divisible by 9

Hence the smallest whole number for x should be 7.

**Question 3 :**

How many three digit numbers are divisible by 5 or 9?

(A) 260 (B) 280 (C) 200 (D) 180

**Solution :**

To find the total number three digit numbers divisible by 5 or 9, let us use the trick given below.

= (Number of 3 digit numbers divisible by 5) + (Number of 3 digit numbers divisible by 9) - (Number of 3 digit numbers divisible both 5 and 9)

**3 digit numbers divisible by 5 :**

100, 105, 110, .............., 995

The sequence is arithmetic progression. To find the number of terms, we use the formula

a_{n } = a + (n - 1) d

a = first term (100)

d = common difference (105 - 100 = 5)

a_{n} = n^{th} term (995)

995 = 100 + (n - 1) 5

895 = 5(n - 1)

n - 1 = 179

n = 180

**3 digit numbers divisible by 9 :**

108, 117, 110, .............., 999

The sequence is arithmetic progression. To find the number of terms, we use the formula

a_{n } = a + (n - 1) d

a = 108, d = 9 and a_{n} = 999

999 = 108 + (n - 1) 9

891 = 9(n - 1)

n - 1 = 99

n = 100

**3 digit numbers divisible by both 5 and 9 :**

If the number is divisible by 45, then it is also divisible by both 5 and 9.

First three digit number divisible by 45 is 135.So the next term of the sequence will be increased by 45.

135, 180, ..........., 990

a_{n } = a + (n - 1) d

a = 135, d = 45 and a_{n} = 990

990 = 135 + (n - 1) 45

990 - 135 = 45(n - 1)

45(n - 1) = 855

n - 1 = 19

n = 20

Number of 3 digit numbers divisible by 5 = 180

Number of 3 digit numbers divisible by 9 = 100

Number of 3 digit numbers divisible both 5 and 9 = 20

Number of three digit numbers divisible by 5 or 9

= 180 + 100 - 20

= 260

Hence the number of three digit numbers divisible by both 5 and 9 is 260.

**Question 4 :**

If x and y are two digits of the number 653xy such that this number is divisible by 80, then x + y = ?

(A) 2 (B) 3 (C) 4 (D) 5

**Solution :**

Factors of 80 are 8 and 10. If the number is divisible by both 8 and 10, we can decide that the given number is divisible by 80.

If the unit digit of the given number is 0, then it is divisible by 10. To check if it is divisible by 8, we have to consider the last three digits of the number.

Let x = 2 and y = 0

Last three digits = 320 (divisible by 8).

So, x + y ==> 2 + 0 ==> 2

Hence the value of x + y is 2.

**Question 5 :**

On dividing a number by 357, we get 39 as remainder. On dividing the same number by 17, what will be the remainder ?

(A) 2 (B) 3 (C) 4 (D) 5

**Solution :**

Let "x" be the required number

Using division algorithm,

Dividend = Divisor x quotient + Remainder

x = 357 q_{1} + 39 -----(1)

x = 17 q_{2} + r -----(2)

If q_{1} = 1, then x = 357(1) + 39

x = 396

If we divide 396 by 17, we will get 5 as remainder.

(We will get the same remainder by applying all the values for q1).

After having gone through the stuff given above, we hope that the students would have practiced questions in the topic divisibility rules.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**