Скачать или смотреть Q10) EX- 3.5 Class 6th Maths Ch 3rd Playing With Numbers | Maths Class 6th CBSE NCERT- By Deepak

Q10) EX- 3.5 Class 6th Maths Ch 3rd Playing With Numbers | Maths Class 6th CBSE NCERT- By Deepak

Students we will learn about the different types of numbers like
A) Even Numbers
b) Odd Numbers
C) Prime Numbers
D) Composite Numbers
and their definitions with examples.

class 6th exercise 3.5 question number 10,
class 6th maths exercise 3.5 question number 10,
class 6th playing with numbers ex 3.5,
6th class maths ex 3.5,

Ramesh has 6 marbles with him. He wants to arrange them in rows in such a way
that each row has the same number of marbles. He arranges them in the following
ways and matches the total number of marbles.
What have we discussed?
1. We have discussed multiples, divisors, factors and have seen how to identify factors
and multiples.
2. We have discussed and discovered the following :
(a) A factor of a number is an exact divisor of that number.
(b) Every number is a factor of itself. 1 is a factor of every number.
(c) Every factor of a number is less than or equal to the given number.
(d) Every number is a multiple of each of its factors.
(e) Every multiple of a given number is greater than or equal to that number.
(f) Every number is a multiple of itself.
3. We have learnt that –
(a) The number other than 1, with only factors namely 1 and the number itself, is a
prime number. Numbers that have more than two factors are called composite
numbers. Number 1 is neither prime nor composite.
(b) The number 2 is the smallest prime number and is even. Every prime number other
than 2 is odd.
(c) Two numbers with only 1 as a common factor are called co-prime numbers.
(d) If a number is divisible by another number then it is divisible by each of the factors
of that number.
(e) A number divisible by two co-prime numbers is divisible by their product also.
4. We have discussed how we can find just by looking at a number, whether it is divisible
by small numbers 2,3,4,5,8,9 and 11. We have explored the relationship between
digits of the numbers and their divisibility by different numbers.
(a) Divisibility by 2,5 and 10 can be seen by just the last digit.
(b) Divisibility by 3 and 9 is checked by finding the sum of all digits.
(c) Divisibility by 4 and 8 is checked by the last 2 and 3 digits respectively.
(d) Divisibility of 11 is checked by comparing the sum of digits at odd and even
places.
5. We have discovered that if two numbers are divisible by a number then their
sum and difference are also divisible by that number.
6. We have learnt that –
(a) The Highest Common Factor (HCF) of two or more given numbers is the highest
of their common factors.
(b) The Lowest Common Multiple (LCM) of two or more given numbers is the lowest
of their common multiples.

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EXERCISE 3.5
1. Which of the following statements are true?
(a) If a number is divisible by 3, it must be divisible by 9.
(b) If a number is divisible by 9, it must be divisible by 3.
(c) A number is divisible by 18, if it is divisible by both 3 and 6.
(d) If a number is divisible by 9 and 10 both, then it must be divisible by 90.
(e) If two numbers are co-primes, at least one of them must be prime.
(f) All numbers which are divisible by 4 must also be divisible by 8.
Write the prime
factorisations of
16, 28, 38.
(g) All numbers which are divisible by 8 must also be divisible by 4.
(h) If a number exactly divides two numbers separately, it must exactly divide their
sum.
(i) If a number exactly divides the sum of two numbers, it must exactly divide the two
numbers separately.
2. Here are two different factor trees for 60. Write the missing numbers.
(a)
(b)
3. Which factors are not included in the prime factorisation of a composite number?
4. Write the greatest 4-digit number and express it in terms of its prime factors.
5. Write the smallest 5-digit number and express it in the form of its prime factors.
6. Find all the prime factors of 1729 and arrange them in ascending order. Now state the
relation, if any; between two consecutive prime factors.
7. The product of three consecutive numbers is always divisible by 6. Verify this statement
with the help of some examples.
8. The sum of two consecutive odd numbers is divisible by 4. Verify this statement with
the help of some examples.
9. In which of the following expressions, prime factorisation has been done?
(a) 24 = 2 × 3 × 4 (b) 56 = 7 × 2 × 2 × 2
(c) 70 = 2 × 5 × 7 (d) 54 = 2 × 3 × 9
10. Determine if 25110 is divisible by 45.
[Hint : 5 and 9 are co-prime numbers. Test the divisibility of the number by 5 and 9].
11. 18 is divisible by both 2 and 3. It is also divisible by 2 × 3 = 6. Similarly, a number
is divisible by both 4 and 6. Can we say that the number must also be divisible by
4 × 6 = 24? If not, give an example to justify your answer.
12. I am the smallest number, having four different prime factors. Can you find me?