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 the first three multiples of each of the following
(i) 11
(ii) 12
Answer:
(i) First three multiples of 11 = 11, 22, 33
(ii) First three multiples of 12 = 12, 24, 36
Question 2.
Write the greatest and the smallest prime number between 10 and 20.
Answer:
Greatest prime number = 19
Smallest prime number =11
Question 3.
Write all the prime numbers between
(i) 10 and 15
(ii) 20 and 35
Answer:
(i) Prime numbers between 10 and 15 = 11, 13
(ii) Prime numbers between 20 and 35 = 23, 29, 31
Question 4.
Which of the following are composite numbers?
7, 13, 16
Answer:
Given numbers are 7,13,16.
Factors of 7 = 1,7
Factors of 13 = 1,13 Factors of 16 = 1, 2, 4, 8, 16
∴ 16 is a composite number.
Question 5.
Write the common factors of 6 and 10.
Answer:
Factors of 6 = 1, 2, 3, 6
Factors of 10 = 1, 2, 5, 10
Common factors of 6 and 10 = 1 and 2
Question 6.
Write the highest common factor of 6 and 15.
Answer:
Factors of 6 = 1, 2, 3, 6
Factors of 15 = 1, 3, 5, 15
Common factors = 1 and 3
Highest common factor = 3
Question 7.
Write the first two common multiples of 5 and 15.
Answer:
Multiples of 5 = 5, 10, 15, 20, 25, 30,…
Multiples of 15 = 15, 30,…
First two common multiples = 15 and 30
Question 8.
Find the prime factorisation of 40.
Answer:
Here, we have 40
40 = 2 × 2 × 2 × 5
Short Answer Type Questions
Question 1.
Give the factorisation of the following numbers.
(i) 136
(ii) 252
Answer:
(i) We have, 136
∴ 136 = 2 × 2 × 2 × 17
(ii) We have, 252
∴ 252 = 2 × 2 × 3 × 3 × 7
Question 2.
Is 12 and 25 are coprime?
Answer:
Yes, they are coprime because they have no common factors other than 1.
Question 3.
Find the common factors of 12 and 18.
Answer:
The common factors of 12 and 18 are 1, 2, 3 and 6.
Question 4.
Is 51 a composite number?
Answer:
Yes, 51 is a composite number because it has factors other than 1 and itself.
Specifically, 51 can be divided by 1, 3, 17 and 51.
Question 5.
Find the prime factorisation of 1600.
Answer:
Prime factorisation of 1600.
1600 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5
Question 6.
What is the test of divisibility for 2?
Answer:
A number is divisible by 2 if its last digit is 0, 2,4, 6 or 8.
Question 7.
Is 72 divisible by 4?
Answer:
Yes, because the last two digits (72) form a number divisible by 4.
Question 8.
Use prime factorisation to check if 2520 and 3003 are
Answer:
Prime factorisation of 2520 and 3003.
2520 = 2 × 2 × 2 × 3 × 3 × 5 × 7
3003 = 3 × 7 × 11 × 13
The common prime factors of 2520 and 3003 are 3 and 7.
Since, they have common prime factors (3 and 7), therefore 2520 and 3003 are not coprime.
Long Answer Type Questions
Question 1.
Find a 4-digit odd number using each of digits 1,2,4 and 5 only once such that when the first and last digits are interchanged, it is divisible by 4.
Answer:
The 4-digit number will be an odd number, if the unit place digit is an odd number (i.e. 1 or 5).
Total such odd numbers are
4125, 4215, 1245, 1425, 2145, 2415, 4251, 4521, 5241, 5421,2451,2541.
Also, we know that any 4-digit number is divisible by 4, if the last two-digit number is divisible by 4.
Consider a number 4521, if we interchage the first and the last digit, the new number will be 1524.
Here, we see that the last two digits (i.e. 24) is divisible by 4.
So, the number 1524 is divisible by 4.
Similarly, other numbers when we interchange the first and the last digit, divisible by 4 are 4125, 2415, 2451.
Hence, the required 4-digit numbers are 4521, 4125, 2415 and 2451.
Question 2.
Find the common prime factors of 120 and 84 and determine if they have any common factors other than 1.
Answer:
Prime factorisation of 120 and 84.
120 = 2 × 2 × 2 × 3 × 5
84 = 2 × 2 × 3 × 7
The common prime factors are 2 and 3.
The common factors other than 1 are 2, 3, 4, 6 and 12.
Question 3.
Identify whether the following numbers are prime or composite : 29, 56, 101 and 77.
For each number provide a brief explanation of why it is classified as prime or composite.
Answer:
For 29, the only divisors are 1 and 29.
Thus, 29 is a prime number.
For 56, the divisors are 1, 2, 4, 7, 8, 14, 28 and 56.
Therefore, 56 is a composite number.
For 101, Since it is not divisible by 2, 3, 5 or 7, it has no divisors other than 1.
Thus, 101 is a prime number.
For 77, it can be divided by 1, 7, 11 and 77.
So, it has other divisors other than 1 and itself.
Therefore, 77 is composite numbers.
Question 4.
Check if the following numbers are divisible by 2, 4 and 5 :144, 250 and 341. For each number, explain how you determine its divisibility by these numbers.
Answer:
For 144
The last digit is 4, therefore 144 is divisible by 2.
The number formed by last two digits (44) is divisible by 4, therefore 144 is divisible by 4.
The last digit is not 0 or 5 , .. therefore 144 is not divisible by 5.
For 250
The last digit is 0, therefore it is divisible by 2.
The number formed by last two digits (50) is not divisible by 4, therefore 144 is not divisible by 4.
The last digit is 0, therefore 144 is divisible by 5.
For 341
The last digit is 1, therefore it is not divisible by 2.
The number formed by last two digits (41) is not divisible by 4, therefore 341 is not divisible by 4.
The last digit is not 0 or 5, therefore 341 is not divisible by 5.
Case-Based Questions
Question 1.
A photographer is hired to take group photographs of students in each class in a school. He arranges the students along with teachers in rows for the photograph. His arrangement has
- atmost 50 people.
- an equal number of people in each row.
A row consists of a minimum of 3 people and a maximum of 8 people.
(i) There are 35 people (students and teachers) in a class for a group photograph. What are the possible arrangements for them?
Answer:
Total number of people (students and teachers) = 35
Factors of 35 are 1, 5, 7 and 35.
Hence, possible arrangements
= 7 rows and 5 students/teachers per row or 5 rows and 7 students/teachers per row
(ii) The photographer arranged some of the students in 6 rows. What can be the maximum number of students in the photograph?
(a) 18
(b) 36
(c) 48
(d) 60
Answer:
(c) The photographer arranged students in 6 rows. Given, maximum number of people in a row = 8
.’. Maximum number of students = 6 x 8 = 48
(iii) How did the students of Class 7 which are 30 in number want to take a photograph along with 2 teachers. Which of the following is the possible arrangement for them?
(a) 2 rows with 16 students in each.
(b) 4 rows with 8 students/teachers in each.
(c) 5 rows with 6 students in each and 1 row for teachers.
Answer:
(b) There are 30 students and 2 teachers in class 7. Thus, in total 32 people.
Let us consider maximum people in a row i.e. 8.
So, divide 32 by 8 to know the number of rows.
32 ÷ 8 = 4
Hence, 4 rows with 8 students/teachers in each.
Question 2.
Ananya is exploring divisibility rules using prime factorisation. She needs to check which numbers are divisible by 12 and 15.
To do this, she first needs to find the prime factorisation of 12 and 15.
Based on the above information, answer the following questions.
(i) What are the prime factors of 12 and 15?
Answer:
Prime factorisation of 12 and 15. s
12 = 2 × 2 × 3
15 = 3 × 5
(ii) Determine of 60 and 90 are divisible by both 12 and 15 using prime factorisation.
Answer:
Prime factorisation of 60 and 90.
60 = 2 × 2 × 3 × 5
90 = 2 × 3 × 3 × 5
So, 60 = 12 × 5 and 60 = 4 × 15
Thus, 60 is divisible by both 12 and 15.
And 90 = 6 × 15
Thus, 90 is divisible by 15 but not 12.
Skill Based Questions
Question 1.
A Prime Puzzle
The figure on the left shows the puzzle. The figure on the right shows the solution of the puzzle. Think what rules can be to solve the puzzle.
Answer:
The rule to solve the puzzle is as follow :
Grid is filled with prime number only so that the product of each row is the number to the right of the row and the product of each column is the number is mentioned below the column.
Question 2.
Solve the following crossword puzzle.
Across
1. Every number is a factor of ………
4. Number which have more than two factors is called ……… numbers.
7. Numbers which have exactly two factors, 1 and the number itself is called …….. numbers.
Down
2. An exact divisor of a number is called …….
3. By multiplying a number by a natural number, we get a ……… of that number.
5. ………. is neither prime nor composite.
6. The smallest natural number is …………
Answer:
2. Across
1. Itself
2. Composite
7. Prime
Down
2. Factor
3. Multiple
5. One
6. One