Finding Common Ground Class 7 Extra Questions Maths Part 2 Chapter 3

Get the simplified Class 7 Maths Extra Questions and Class 7 Maths Part 2 Chapter 3 Finding Common Ground Extra Questions and Answers with complete explanation.

Class 7 Finding Common Ground Extra Questions

Finding Common Ground Extra Questions Class 7

Finding Common Ground Class 7 Very Short Question Answer

Question 1.
Find the common factors of 12 and 18.
Solution :
factors of 12 = 1,2,3,4,6,12
factors of 18 = 1,2,3,6,9,18
Common factors = 1,2,3,6

Question 2.
Find the HCF of 8 and 20
Solution :
factors of 8 = 1,2,4,8
factors of 20 = 1,2,4,5,10,20
HCF = 4

Question 3.
Find HCF of 45 and 60 using prime factorisation.
Solution :
factors of 45 = 3 × 3 × 5
factors of 60 = 2 × 2 × 3 × 5
Common factors = 3 × 5
∴ HCF = 15

Question 4.
Find the LCM of 12 and 15.
Solution :
factors of 12 = 2 × 2 × 3
factors of 15 = 3 × 5
∴ LCM = 2 × 2 × 3 × 5 = 60

Question 5.
If HCF = 5 and LCM = 60, find the product of the two numbers.
Solution :
Product = HCF × LCM
= 5 × 60 = 300

Question 6.
The product of two numbers = 180 and HCF = 6. Find LCM.
Solution :
LCM = Product ÷ HCF
= 180 ÷ 6 = 30

Question 7.
Two numbers have HCF = 12 and LCM = 180. One number is 36. Find the other.
Solution :
Other number

Finding Common Ground Class 7 Short Question Answer

Question 1.
The HCF of two numbers is 5 and their LCM is 60. If one number is 15, what will be the other number?
Solution :
We know that HCF × LCM = Number 1 × Number 2
5 × 60 = 15 × Number 2
300 = 15 × Number 2
Therefore, Number 2 = \(\frac{300}{15}\) = 20

Question 2.
Find the LCM of 20 and 32.
Solution :
Step 1: Write the numbers in the same row.
Step 2: Start dividing the numbers with the smallest prime number which divides at least one or all the given numbers.
Step 3: If the number is not divisible by the prime number, bring the number down, as it is.
Step 4: Repeat the process of division, till all the numbers are reduced to 1.
Step 5: Multiply all the prime numbers in the left column and find the LCM.
LCM of 20 and 32 is 2 × 2 × 2 × 2 × 2 × 5 = 160.

Question 3.
Write the prime factors of the number 48 by the division method.
Solution :
Step 1: We first divide the number by the first prime number, i.e., 2. (divide only if it divides the number completely without leaving a remainder)
Step 2: Now, divide the quotient again by the prime number completely, without leaving a remainder.
Step 3: Continue the process of division until the quotient is 1.
Hence, 2, 2, 2, 2, 3 are the prime factors of 48.
We can cross-check the answer by multiplying all the factors.

Question 4.
What is the smallest number that is a multiple of 2,3,5,7,8, and 12?
Solution :
We must find the LCM (Least Common Multiple) of :
2, 3, 5, 7, 8, 12
Prime factorisation of numbers :
2 = 2
3 = 3
5 = 5
7 = 7
8 = 2³
12 = 2² × 3
LCM = 2³ × 3 × 5 × 7
= 8 × 3 × 5 × 7
= 840
The smallest number that is a multiple of 2, 3, 5, 7, 8 and 12 is 840.

Question 5.
Find two numbers whose HCF is 1 and LCM is 84.
Solution :
We use the formula :
HCF × LCM = Product of the two numbers
Given:
HCF = 1
LCM = 84
1 × 84 = 84
Since the HCF is 1, the two numbers must be co-prime and their product must be 84.
Factorise 84 :
84 = 4 × 21
Check if 4 and 21 have common factors :
Factors of 4 = 1,2,4
Factors of 21 = 1,3,7,21
Common factor = 1 only
So, the two required numbers are: 4 and 21.

Question 6.
(a) Is 3 × 5 × 5 × 7 a multiple of 3 × 5 × 7 × 2 × 2 ?
(b) Is 3 × 5 × 5 × 7 a factor of 3 × 5 × 7 × 2 × 2 ?
Solution :
(a) To be a multiple, the first number must contain all prime factors of the second number in the same or greater powers. The second number contains 2², but the first number has no factor 2 at all.
So the first number is not a multiple of the second.
(b) To be a factor, the second number must contain all prime factors of the first number in the same or greater powers.
The first number contains 5², but the second has only 5¹.
So the first number is not a factor of the second.

Question 7.
Find the HCF and LCM of the following numbers. (State your answers in the form of prime factorisation.)
(a) 2 × 3 × 3 × 5 × 7 and 3 × 5 × 7 × 11
(b) 48 and 54
Solution :
(a) First number: 2 × 3² × 5 × 7
Second number : 3 × 5 × 7 × 11
Find HCF: Take common prime factors with the lowest powers :
Common primes : 3, 5, 7
HCF = 3 × 5 × 7
Find LCM: Take all prime factors with their highest powers :
LCM = 2 × 3² × 5 × 7 × 11

(b) Prime factors of both numbers
48 = 2⁴ × 3
54 = 2 × 3³
HCF = 2 × 3
LCM = 2⁴ × 3³