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ML Aggarwal Class 6 Solutions Chapter 4 Playing with Numbers Ex 4.3 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 4 Playing with Numbers Ex 4.3

Question 1.
Here are two different factor trees of the number 90. Write the missing numbers:

Solution:

Question 2.
Find the prime factorisation of the following numbers:
(i) 72
(ii) 172
(in) 450
(iv) 980
(v) 8712
(vi) 13500
Solution:

Question 3.
Write the smallest and the greatest 3-digit numbers and express them as the product of prime.
Solution:

Question 4.
Write the smallest five digit number and express it in the form of its prime factors.
Solution:

Question 5.
1 am the smallest number, having four different prime factors. Can you find me?
Solution:

ML Aggarwal Class 6 Solutions Chapter 4 Playing with Numbers Ex 4.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 4 Playing with Numbers Ex 4.2

Question 1.
Which of the following numbers are divisible by 5 or by 10:
(i) 3725
(ii) 48970
(iii) 56823
(iv) 760035
(v) 7893217
(vi) 4500010
Solution:

Question 2.
Which of the following numbers are divisible by 2, 4 or 8:
(i) 54014
(ii) 723840
(iii) 6531088
(iv) 75689604
(v) 786235
(vi) 5321048
Solution:

Question 3.
Which of the following numbers are divisible by 3 or 9:
(i) 7341
(ii) 59031
(iii) 12345678
(iv) 560319
(v) 720634
(vi) 3721509
Solution:

Question 4.
Examine the following numbers for divisibility by 11:
(i) 10428
(ii) 70169803
(iii) 7136985
Solution:

Question 5.
Examine the following numbers for divisibility by 6:
(i) 93573
(ii) 217944
(iii) 5034126
(iv) 901352
(v) 639210
(vi) 1790184
Solution:

Question 6.
In each of the following replace ‘*’ by a digit so that the number formed is divisible by 9:
(i) 4710 * 82
(ii) 70 * 356722
Solution:

Question 7.
In each of the following replace ‘*’ by (i) the smallest digit (ii) the greatest digit so that the number formed is divisible by 3:
(a) 4 * 672
(b) 4756 * 2
Solution:

Question 8.
In each of the following replace ‘*’ by a digit so that the number formed is divisible by 11:
(i) 8 * 9484
(ii) 9 * 53762
Solution:

Question 9.
In each of the following replace ‘*’ by (i) the smallest digit 00 the greatest digit so that the number formed is divisible by 6:
(a) 2 * 4706
(b) 5825 * 34
Solution:


Question 10.
Which of the following numbers are prime:
(i) 101
(ii) 251
(iii) 323
(iv) 397
Solution:

Question 11.
Determine if 372645 is divisible by 45.
Solution:

Question 12.
A number is divisible by 12. By what other numbers will that number be divisible?
Solution:

Question 13.
A number is divisible by both 3 and 8. By which other numbers will that number be always divisible?
Solution:

Question 14.
State whether the following statements are true (T) or false (F):
(i) If a number is divisible by 4, it must be divisible by 8.
(ii) If a number is divisible by 3, it must be divisible by 9.
(iii) If a number is divisible by 9, it must be divisible by 3.
(iv) If a number is divisible by 9 and 10 both, it must be divisible by 90.
(v) If a number divides two numbers separately, then it must divide their sum.
(vi) If a number divides the sum of two numbers, then it must divide the two numbers separately. .
(vii) If a number is divisible by 3 and 8 both, it must be divisible by 12.
(viii) If a number is divisible by 6 and 15 both, it must be divisible by 90.
Solution:

ML Aggarwal Class 6 Solutions Chapter 4 Playing with Numbers Ex 4.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 4 Playing with Numbers Ex 4.1

Question 1.
Fill in the blanks:
(i) A number having exactly two factors is called a …..
(ii) A number having more than two factors is called a ………
(iii) 1 is neither ……… nor ………
(iv) The smallest prime number is ………
(v) The smallest odd prime number is ………
(vi) The smallest composite number is ………
(vii) The smallest odd composite number is ………
(viii) All prime numbers (except 2) are ………
Solution:

Question 2.
State whether the following statements are ture (T) or false (F):
(i) The sum of three odd numbers is an even number.
(ii) The sum of two odd numbers and one even number is an even number.
(iii) The product of two even numbers is always an even number.
(iv) The product of three odd numbers is an odd number.
(v) If an even number is divided by 2, the quotient is always an odd number.
(vi) All prime numbers are odd.
(vii) All even numbers are composite.
(viii) Prime numbers do not have any factors.
(ix) A natural number is called a composite number if it has atleast one more factor other than 1 and the number itself.
(x) Two consecutive numbers cannot be both prime.
(xi) Two prime numbers are always co-prime numbers.
Solution:

Question 3.
Write all the factors of the following natural numbers:
(i) 68
(ii) 27
(iii) 210
Solution:

Question 4.
Write first six multiples of the following natural numbers:
(i) 3
(ii) 5
(iii) 12
Solution:

Question 5.
Match the items in column 1 with the items in column 2:

Solution:

Question 6.
Find the common factors of :
(i) 20 and 28
(ii) 35 and 50
(iii) 56 and 120
Solution:

Question 7.
Find the common factors of:
(i) 4, 8, 12
(ii) 10, 30 and 45
Solution:

Question 8.
Write all natural numbers less than 100 which are common
multiples of 3 and 4.
Solution:

Question 9.
(i) Write the odd numbers between 36 and 53.
(ii) Write the even numbers between 232 and 251.
Solution:

Question 10.
(i) Write four consecutive odd numbers succeeding 79.
(ii) Write three consecutive even numbers preceding 124.
Solution:

Question 11.
What is greatest prime number between 1 and 15?
Solution:

Question 12.
Which of the following numbers are prime?
(i) 29
(ii) 57
(iii) 43
(iv) 61
Solution:

Question 13.
Which of the following pairs of numbers are co-prime?
(i) 12 and 35
(ii) 15 and 37
(iii) 27 and 32
(iv) 17 and 85
(v) 515 and 516
(vi) 215 and 415
Solution:

Question 14.
Express each of the following numbers as the sum of two odd primes:
(i) 24
(ii) 36
(iii) 84
(iv) 98
Solution:

Question 15.
Express each of the following numbers as the sum of twin-primes:
(i) 24
(ii) 36
(iii) 84
(iv) 120
Solution:

Question 16.
Express each of the following numbers as the sum of three odd primes:
(i) 21
(ii) 35
(iii) 49
(iv) 63
Solution:

ML Aggarwal Class 6 Solutions Chapter 3 Integers Check Your Progress for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 3 Integers Check Your Progress

Question 1.
Use the appropriate symbol < or > to fill in the following blanks:
(i) (-3 + ……… (-6) (-3) – (-6)
(ii) (-21) – (-10) ……. (-31)+ (-11)
(iii) 45 – (-11) ……….. (57) + (-4)
(iv) (-25) – (-42) …………. (-42) – (-25)
Solution:

Question 2.
Find the value of:
(i) 12 + ( -3) + 5 – (-2)
(ii) 39 – 35 + 7-(-4) + 21
(iii) -15- (-2) – 71 – 8 + 6
Solution:

Question 3.
Evaluate:
(i) |-13| – |-15|
(ii) |35 – 41| – |7-(-2)|
Solution:

Question 4.
Arrange the following integers in ascending order:
-39, 35, -102, 0, -51, -5, -6, 7
Solution:

Question 5.
Find the successor and the predecessor of -199.
Solution:

Question 6.
Subtract the sum of -235 and 137 from -152.
Solution:

Question 7.
What must be added to -176 to get -95?
Solution:

Question 8.
What is the difference in height between a point 270 m above sea level and 80 m below sea level?
Solution:

ML Aggarwal Class 6 Solutions Chapter 3 Integers Objective Type Questions for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 3 Integers Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) The absolute value of 0 is ………
(ii) The sum of two negative integers is always a ……….. integer.
(iii) The smallest positive integer is ……………
(iv) The largest negative integer is ………….
(v) 17 + ………….. = 0
(vi) ……………. -15 = -10
(vii) The predecessor of -99 is …………
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) The sum of a positive integer and a negative integer is always a negative integer.
(ii) Zero is an integer.
(iii) The sum of an integer and its negative is always zero.
(iv) The sum of three integers can never be zero.
(v) |-7| < |-3|.
(vi) -20 is to the left of -21 on the number line.
(vii) The successor of -29 is -30.
(viii) 0 is greater than every negative integer.
(ix) The difference of two integers is always an integer.
(x) Additive inverse of a negative integer is always a positive integer.
Solution:

Question 3.
State whether the following statements are true or false. If a statement is false, write the corresponding correct statement.
(i) -8 is to the right of-10 on the number line.
(ii) -100 is to the right of -50 on the number line.
(iii) Smallest negative integer is -1.
(iv) -26 is greater than -25.
(v) -187 is the predecessor of-188.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (4 to 17):
Question 4.
The integer which is 5 more than -2 is
(a) -7
(b) -3
(c) 3
(d) 7
Solution:

Question 5.
The number of integers between -1 and 1 is
(a) 0
(b) 1
(c) 2
(d) 3
Solution:

Question 6.
The number of integers between -3 and 2 are
(a) 2
(b) 3
(c) 4
(d) 5
Solution:

Question 7.
The number of whole numbers between -6 and 6 is
(a) 11
(b) 10
(c) 6
(d) 5
Solution:

Question 8.
The greatest integer lying -10 and -15 is
(a) -10
(b) -11
(c) -14
(d) -15
Solution:

Question 9.
The smallest integer lying between -10 and -15 is
(a)-10
(b) -11
(c) -14
(d) -15
Solution:

Question 10.
Which of the following statement is true?
(a) |10 – 4| = |10| + |—4|
(b) Additive inverse of -5 is 5
(c) -1 lies on the right of 0 on the number line
(d) -7 is greater than -3
Solution:

Question 11.
Which of the following statement is false?
(a) -20 – (-5) = -15
(b) |-18| > |-13|
(c) 23 + (-31) = 8
(d) Every negative integer is less than 5
Solution:

Question 12.
Which of the following statements is false?
(a) (-3) + (-11) is an integer
(b) (-19)+ 13 = 13 +(-19)
(c) (-15) + 0 = -15 = 0 + (-15)
(d) Negative of-7 does not exist
Solution:

Question 13.
If the sum of two integers is -17 and one of them is -9, then the other is
(a) 8
(b) -8
(c) 26
(d) -26
Solution:

Question 14.
On subtracting -7 from -4, we get
(a) 3.
(b) -3
(c) -11
(d) none of these
Solution:

Question 15.
(-12) + 17 – (-10) is equal to
(a) -5
(b) 5
(c) 15
(d) -15
Solution:

Question 16.
Which of the following statements is true?
(a) -13 > – 8 – (-6)
(b) -5 – 4 > -12 + 2
(c) (-8) – 3 = (-3) – (-8)
(d) (-15) – (-22) < (-22) – (-15)
Solution:

Question 17.
The statement “when an integer is added to itself, the sum is less than the integer” is
(a) always true
(b) never true
(c) true only when the integer is negative
(d) true when the integer is zero or positive
Solution:

Higher Order Thinking Skills (HOTS)
Question 1.
Can the sum of successor and predecessor of an integer be an odd integer?
Solution:

Question 2.
What is the sum of all integers from -500 to 500?
Solution:

Question 3.
Find two positive integers such that their product is 1,00,000 and none of them contains 0 as a digit.
Solution: