1. Write the greatest 4 digit number and
express it in the form of its prime factors.

2. Find the largest number which is a
factor of each of the numbers 504,792 and 1080

3. The length, breadth and height of a
room are 12m,15m and 18 m respectively,
Determine the longest tape which can measure all the three dimensions of
the room exactly.

4. Check whether the following numbers are
divisible by 11.

1) 859484, ii) 10824 iii) 20801

5. Find the smallest number which when
added to 5 is exactly divisible by 12,14,and 18.

6. Find the greatest 3 digit number
which when divided by 75,45 and 60
leaves (i) no remainder (ii) the remainder 4 in each case

7. Three measuring tapes are 64cm, 72 cm
and 96 cm. What is the least length that can be measured by any one of the
tapes exactly?

8. Write the nearest number to 1240
which is divisible by 11?

9. Find the smallest number that must be
added to 123, so that it becomes exactly divisible by 5

10.
What is the greatest Prime number between 1
and 20?

11.
Write
three pairs of prime numbers less than 20 whose sum is divisible by 5?

12.
The
LCM of two numbers is 290 and their product is 7250, what will be its HCF?

13.
The product of two numbers is 3276 if their HCF is 6 find their LCM.

14.
The
HCF of two numbers is 6 and their LCM is 36.
If one of the numbers is 12, find the other.

15.
Find
the smallest number that can be subtracted from 1965, so that it becomes
divisible by 4?

16.
Find
the HCF of 12,16 and 28 by prime factorization method

17.
Is
100000 is divisible by 4 ? why?

18.
Is
9876104 divisible by 8?

19.
7224
divisible by 6 ? why?

Om Sri Ram, Om Sri Ram Om Sri Ram

1. Write the greatest 4 digit number and
express it in the form of its prime factors.

Ans. The greatest four degit number is “9999”

3)9999

3)3333 9999= 3x3x11x101

11)1111

--------

101

-------

2. Find the largest number which is a
factor of each of the numbers 504,792 and 1080

Ans. Let us find the HCF of 504 and 792

504)792 (1

504

-------

288 ) 504 (1 72)1080(14

288 1008

------- ----------

216 ) 288
( 1 72 )
72 ( 1

216 72

-------
----------

72 ) 216 (3 0

216

-------

3. The length, breadth and height of a
room are 12m,15m and 18 m respectively,
Determine the longest tape which can measure all the three dimensions of
the room exactly.

Ans. 12 = 2x2 x3 , 15 = 3 x
5 18 = 2 x 3 x 3

Now H.C.F. = 3

4. Check whether the following number are divisible by 11.

1) 859484,

Ans. 859484

The sum of the digits at odd
places =4+4+5=13

The sum of the digits at even
places=8+9+8=25

Their difference = 25 – 13 =
12,

The difference is not Zero,
now not divisible by 11

5. Find the smallest number which when
added to 5 is exactly divisible by 12,14,and 18.

Ans. 2)12, 14, 18

3)06, 07, 09

---------------

2,7,3 L.C.M. 2 x 3x 2x 7x 3= 252

Required smallest number – 252-5 =247

6. Find the greatest 3 digit number
which when divided by 75,45 and 60
leaves (i) no remainder (ii) the remainder 4 in each case

Ans. I) 75, 45, 60 L.C. = 5 x3x 5x 3 x4=900

The required number with no remainder
=900

ii) DThe required number
with remainder 4 in each

case = 900 + 4 = 904

7. Three measuring tapes are 64cm, 72 cm
and 96 cm. What is the least length that can be measured by any one of the
tapes exactly?

2)64, 72, 96

2)32, 36, 48 L.C.M
2x2x2x2x2x2x3x3 = 576 Cm.

2)16, 18, 24

2)08, 09, 12

2)04, 09, 06

2)02, 09, 03

3)02, 03, 01

2)01, 03, 01

3)01, 01, 01

8. Write the nearest number to 1240
which is divisible by 11?

Ans. 11 x 112 = 1232

11 x 113= 1243

9. Find the smallest number that must be
added to 123, so that it becomes exactly divisible by 5

Ans. Then the number becomes 123+2 =125

Now 5 is devisible.

10.
What is the greatest Prime number between 1
and 20 ?

Ans. 1 and 20 are
2,3,5,7,11,13,17,19, The greatest prime

number is 19

11.
Write
three pairs of prime numbers less than 20 whose sum is divisible by 5?

Ans. (3,7), (7,13),(17,3) The sum of each pair divisible by 5.

12.
The
LCM of two numbers is 290 and their productis 7250, what will be its HCF?

Ans. 290 x HCF = 7250

HCF = 7250/290 = 25

13.
The
product of two numbers is 3276 if their HCF is 6 find their LCM.

Ans. Product of two numbers = 3276, HCF = 6 LCM= ?

L.C.M. x H.C.F. = product
of two numbers

L.C.M = 3276/6 =546

14.
The
HCF of two numbers is 6 and their LCM is 36.
If one of the numbers is 12, find the other.

Ans. HCF.6,LCM.36, one number is
12, 2

^{nd}number is “x”
HCF x LCM = 12 x x , x= 6x36/12 = 18

15.
Find
the smallest number that can be subtracted from 1965, so that it becomes
divisible by 4?

Ans. The last two digits is 65. Subtracted is “1” =64 we know that 1964
is devisible by 4

16.
Find
the HCF of 12,16 and 28 by prime factorization method

2)12
2)16 2)28

2)06 2)08 2)14

3)03 2)04 7)07

---- 2)02 -----

01 -------- 01

01

12= 2x2x3
16=2x2x2x2 28=2x2x7

The common factor is 2x2 =4

17.
Is
100000 is divisible by 4 ? why?

Ans. 100000 = 1000 x 100

Now 100 devisible by
4 i.e. 100000 is devisible by 4

18.
Is
9876104 divisible by 8?

Ans. Given the number last 3 digits “104” It is devisible by

8, The given the no. is
devisible by 8

19.
7224
divisible by 6 ? why?

Ans. Units place is 4, it is devisible by 2

The sum of the degits
7+2+2+4=15

“15” is multiple of 3 ,
given number 2 &3 is divisible

now 6is divisible.

20.
Write
a polyndrome number of six digits.

Ans. The six digited polyndrome number is “ 123321”