Class 6 Maths Chapter 5 Extra Questions Prime Time
Class 6 Maths Prime Time Extra Questions
NCERT Class 6 Maths Chapter 5 Prime Time Extra Questions and Answers
Very Short Answer Type Questions
Question 1.
Write first five multiples of 17.
Solution :
The first five multiples of 17 are
17 × 1 ; 17 × 2 ; 17 × 3 ; 17 × 4 ; 17 × 5
∴ 17,34,51,68,85 are multiple of 5
Question 2.
Write all factors of 24.
Solution :
24 = 1 × 24
= 2 × 12
= 3 × 8
= 4 × 6
So factors of 24 are 1,2,3,4,6,8,12,24.
Question 3.
Express 44 as a sum of two primes.
Solution :
44 = 3 + 41 or 7 + 37
Short Answer Type Questions
Question 1.
Make factor tree for 240.
Solution :
Thus, 240 = 2 × 2 × 2 × 2 × 3 × 5
Question 2.
Photographs are sold in small, medium and large sizes. The cost of photographs according to their size is given in the tables below;
Photograph size | Cost(Rs.) |
Small | 50 |
Medium | 80 |
Large | 100 |
150 photographs worth Rs. 10,250 were sold. If 75 of them were of small size, find how many large size photographs were sold?
Solution :
If there are 150 photographs and 75 were small Now, remaining 75 photographs will be medium and large.
Money collected by selling 75 small photographs
= 75 × 50 = ₹ 3750
Total money collected = ₹ 10250
So, money collected by selling medium and large photographs
= ₹ 6500
Now, the number of photographs of medium and large size must be such that they satisfy the criterion that x + y = 75 and 80 x + 100 y = 6500
where x is the number of medium photographs and y is the number of large photographs.
On solving, the number of large photographs is 25.
Passage Based Questions
Passage 1 : A florist had 200 roses, 180 marigold and 320 orchids with him. He was asked to make garlands of flowers with only roses or only marigold or only orchids each containing the some number of flowers.
Question 1.
The correct prime factorisation of 180 is:
(a) 2 × 2 × 3 × 3 × 5
(b) 4 × 3 × 3 × 5
(c) 2 × 2 × 9 × 5
(d) 4 × 9 × 5
Answer:
Option (a) is correct.
Explanation: Option (a) has all the factors prime numbers. So it is the correct factorisation of 180.
Question 2.
The LCM of two coprime numbers is equal to
(a) 1
(b) the greatest number
(c) their product
(d) odd
Answer:
Option (c) is correct.
Explanation: The LCM of two coprime numbers is their product.
Question 3.
What will be the largest number of flowers he can join together without leaving a single flower.
Answer:
To find, how many factors are common, firstly we find factors as:
320 = 2 × 2 × 2 × 2 × 2 × 2 × 5
So, common factors to all are =2 × 2 × 5=20 Hence largest number of flowers is 20.
Passage-2 : In a school library, there are 780 books of English and 364 books of Science. Ms. Yakang, the librarian of the school wants to store these books in shelves such that each shelf should have the same number of books of each subject.
Question 1.
What is the prime factorisation of 780 and 364. ?
Answer:
Factors of 780 = 2 × 2 × 3 × 5 × 13
And 364 = 2 × 2 × 7 × 13
Question 2.
What should be the minimum number of books in each shelf?
Answer:
By given value in school library
Factorisation of 780 = 2 × 2 × 3 × 5 × 13
And 364 = 2 × 2 × 7 × 13
The common factors are 2 × 2 × 13 = 52
So, the minimum number of books in each shelf is 52.
Question 3.
How many factors are common in 780 and 364. ?
Answer:
Common factors are 2 and 13
So, there are two common factors.
In the following questions, out of the four options, only one is correct. Write the correct answer.
Question 1.
Number of even numbers between 58 and 80 is
(a) 10
(b) 11
(c) 12
(d) 13
Answer:
Option (a) is correct.
Explanation: Even numbers between 58 and 80 are 60,62,64,66,68,70,72,74,76, and 78.
So, there are 10 even numbers.
Question 2.
Sum of the number of primes between 16 to 80 and 90 to 100 is
(a) 20
(b) 18
(c) 17
(d) 16
Answer:
Option (c) is correct.
Explanation: Prime numbers between 16 and 80 are 17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79
Prime Number between 90 and 100 is 97.
So, sum of number of primes =16+1=17
Question 3.
The number of distinct prime factors of the largest 4-digit number is
(a) 2
(b) 3
(c) 5
(d) 11
Answer:
Option (b) is correct.
Explanation: 9999 is the greatest 4 digit number.
9999 = 3 × 3333 = 3 × 3 × 1111 = 3 × 3 × 11 × 101
9999 = 3 × 3 × 11 × 101
3 distinct prime factor are 3,11 and 101.
Question 4.
The number of distinct prime factors of the smadlest 5 -digit number is
(a) 2
(b) 4
(c) 6
(d) 8
Answer:
Option (a) is correct.
Explanation: The smallest 5-digit number is 10000 And its prime factorization is 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5
Distinct prime factors are 2 and 5.
Question 5.
A number is divisible by 5 and 6. It may not be divisible by
(a) 10
(b) 15
(c) 30
(d) 60
Answer:
Option (d) is correct.
Explanation: The multiple of 5 and 6 is 30 it is divisible by 10,15 , and 30 but not 60.
True/False
Question 1.
Every multiple of a number is greater than or equal to the number.
Answer:
True
Question 2.
The number of multiples of a’given number is finite.
Answer:
False
Question 3.
Every number is a multiple of itself.
Answer:
True
Question 4.
If a number is divisible by 2 and 3 , then it is also divisible by 6 . So, if a number is divisible by 2 and 4 , it must be divisible by 8.
Answer:
False [2 and 4 are not co-primes]
Fill in the Blanks
Question 1.
A number is a _____ of each of its factors.
Answer:
Multiple
Question 2.
_____ is a factor of every number.
Answer:
1
Question 3.
The number of factors of a prime number is. _____.
Answer:
2
Question 4.
A number for which the sum of all its factors is equal to twice the number is called a. ______ number.
Answer:
Perfect
Question 5.
The numbers having more than two factors are called ______ numbers.
Answer:
Composite