MATHEMATICS ASSIGNMENT
CHAPTER1 [NUMBER SYSTEM] CLASS X
Mathematics assignment for class X chapter 1 Real Numbers with answers and hints for the solution. Extra questions of chapter 1 real number class X
Note: * Marked questions are Excluded the CBSE syllabus For complete explanations and basics related to the number system: Click Here
Math Assignment Chapter 1 Class X : Real Number System
Level  1
Q1 Define Fundamental theorem of Arithmetic’s, HCF & LCM .
Solution: Fundamental theorem of Arithmetic’s :
Every composite number can be expressed as the product of primes and this factorization is unique, irrespective of their order.
HCF : HCF is the product of common factors with smallest powers.
LCM : LCM is the product of all factors with largest powers.
Q2) Find the HCF of the following by using Fundamental Theorem of Arithmetic's .
a) 650, 1170 Ans HCF = 130,
b) 963, 657 Ans HCF = 9,
c) 592 , 252 Ans 4
d) 315 , 198 Ans 9
e) 180 , 192 Ans 12
f) 216 , 1176 Ans 24
g) 4052 , 12576 Ans 4
h) 136, 170 , 255 Ans 17
I) 506 , 1155 Ans 11
j) 1288 , 575 Ans 23
k) 180, 252 , 324 Ans 36
l) 184 , 230 , 276 Ans 46
Question 3: Express the following as the
product of primes
a) 156 b) 5005 c) 7429 d) 1008 e) 364 f) 429 g) 10626
Question 4: Use FTA & Find HCF & LCM
of the following
a) 510 , 92 Ans HCF = 2, LCM = 23460
b) 336, 54 Ans HCF = 6, LCM = 3024
c) 225 , 450 Ans HCF = 225, LCM = 450
d) 1440 , 1800 Ans HCF = 360, LCM = 7200
e) 40, 36 , 126 Ans HCF = 2, LCM = 2520
f) 25, 40 , 60 Ans HCF = 5, LCM = 600
g) 72, 80, 120 Ans HCF = 8, LCM = 720
h) 84, 90 , 120 Ans HCF = 6, LCM = 2520
Question 5
Given that LCM(989, 1892) is 43516, find HCF.
Ans 43
Question 6
HCF (45 and 105) = 15 find their LCM
Ans: 315
Question 7
Given that LCM(77, 99) = 693. Find HCF.
Ans: 11
Question 8
Given that HCF(x, 657) = 9 and LCM(x, 657) = 22338. Find x.
Ans 306
Question 9: Prove the following are irrational
number
S N

Questions

S N

Questions

S N

Questions

a


e


i


b


f


j


c


g




d


h




Question 10
If HCF(6, x) = 2 and LCM(6, x) = 60. Find x.
Ans 20
Question 11
If HCF(48, x) = 24 and LCM(48, x) = 144, find x.
Ans 72
Question 12
Check whether 12ⁿ can end with the digit 0 ∀n ϵ N.
Question 13
Check whether 39ⁿ is divisible by 3.
Question 14
What is the exponent of 3 in the prime factorization of 864.
Question 15
What is the HCF × LCM for 105 and 120.
Question 16
Can two numbers have 15 as their HCF and 175 as their LCM ? Give reasons.
Answer: 175 is not divisible by 15, so it is not possible to have two numbers which have 15 as their HCF and 175 as their LCM
Note: LCM is always the multiple of HCF. So if we divide LCM of two numbers by their HCF then remainder should be zero.
Question 17
Show that 2 x 3 x 4 x 5 x 6 x 7 + 5 x 6 is a composite number.
Hint: Composite Numbers: The numbers which have more than two factors are called composite numbers.
Question 18
Write whether given a rational or an irrational number.
Ans Rational
Hint: Simplify the above number we get a rational number
Question 19
Find the smallest number which leaves remainder 8 and 12 when divided by 28 and 32 respectively . Ans 204
[Hint 28 – 8 = 20, 32 – 12 = 20, Required No = LCM(28, 32) 20]
Question 20
What is the smallest number which, when divided by 35, 56, 91 leaves remainder 7 in each case. Ans 3647
Question 21
Find the greatest number that will divide 445, 572 and 699 leaving remainders 4, 5 and 6 respectively. Ans 63
Question 22
Find the greatest number which on dividing 1657 and 2037 leaves remainder 6 and 5 respectively. Ans 127
Question 23
Find the greatest number of 6 digit which is exactly divisible by 24, 15 and 36
Ans 999720
Question 24
Length, breadth and height of a room are 8 m 25 cm, 6 m 75 cm and 4 m 50 cm respectively. Find the length of the longest rod which can measure the three dimensions of the room exactly.
Answer: 75 cm
Question 25
Find the greatest number which when divides 2011 and 2623 leaving remainder 9 and 5 respectively
Ans 154
Question 26
Find the largest number which on dividing 1251, 9377 and 15628 leaves remainder 1, 2, and 3 respectively.
Ans 625
Question 27
On a morning walk, three persons step out together and their steps measure 30 cm, 36 cm and 40 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps.
Ans 360
QUESTIONS DELETED FROM CBSE SYLLABUS
* Q28 State whether the following are terminating or nonterminating, if terminating then convert these into decimals.
a) Ans Terminating 0.45
b) Ans nonterminating but repeating decimal
c) Ans Terminating
d) Ans Terminating
e) Ans Terminating
f) Ans Terminating 40.6
* Question 29
Show that any positive even integer is of the form 4q or 4q + 2.
* Question 30
Show that any positive even integers is of the form 6q, 6q + 2, 6q + 4.
* Question 31
Use E.D.A to show that square of any positive integer is either of the form 3m, 3m + 1 for some integer m.
* Question 32
Use E.D.A to show that cube of any positive integer is either of the form 9m, 9m + 1, 9m + 8.
* Question 33
If HCF of 144 and 180 is expressed in the form 13m – 3 , then find the value of m.
Ans 3
* Question 34
If HCF of 65 and 117 is expressible in the form 65n  117, then find the value of n.
Ans n = 2
* Question 35
Find the HCF of 65 and 117 and find the value of m and n if HCF = 65m + 117n
Ans m = 2, n =  1
* Question 36
By Using EDA, find whether 847, 2160 are coprimes or not
Ans Yes these are coprime because their HCF = 1
* Question 37
Given The decimal expansion of above given number will terminate after how many places of decimals.
Ans 4
* Question 38
If HCF of 81 and 237 be expressed as 81x + 237y then find the value of x and y
Ans x =  38, y = 13
* Question 39
Show that one and only one out of n, n + 4, n + 8, n + 12, n + 16 is divisible by 5. Where n is any positive integer.
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