Well-designed AP 6th Class Maths Solutions Chapter 3 Playing with Numbers InText Questions offers step-by-step explanations to help students understand problem-solving strategies.
AP 7th Class Maths 3rd Chapter Playing with Numbers InText Questions
Try these (Page No : 60)
Question 1.
Observe that 2 × 3 + 1 = 7 is a prime number. Here, 1 has been added to a multiple of 2 to get a prime number. Can you find some more numbers of this type ?
Solution:
2 × 5 + 1 = 11 is also an prime number and 2 × 6 + 1 = 13 is also an prime number.
Try these（Page No: 72)
Question 1.
Find the common factors of.
a) 8,20
Solution:
Given numbers are 8, 20.
Factors of 8 = 1,2,4,8 [∵ 1 × 8 = 8; 2 × 4 = 8]
Factors of 20 = 1,2,4,5,10,20
[∵ 1 × 20 = 20; 2 × 10 = 20; 4 × 5 = 20]
Hence, common factors of 8 and 20 are 1,2 and 4.
b) 9,15
Solution:
Given numbers are 9 and 15.
Factors of 9 = 1,3,9
[∵ 1 × 9 = 9; 3 × 3 = 9]
Factors of 15 = 1,3,5,15
[∵ 1 × 15 = 15; 3 × 5 = 15]
Hence, common factors of 9 and 15 are 1 and 3.
Try these (Page No: 76)
Question 1.
Write the prime factorisations of 16 , 28, 38.
Solution:
i) Given number = 16
Hence, the prime factorisation of 16 = 2 × 2 × 2 × 2
ii) Given number = 28
Hence, the prime factorisation of 28 = 2 × 2 × 7
iii) Given number = 38
Hence, the prime factorisation of 38 = 2 × 19
Try these (Page No: 80)
Question 1.
Find the HCF of the following :
i) 24 and 36
Solution:
Finding the prime factors of 24 and 36, we get
The common factors of 24 and 36 are 2 (occurrence twice) and 3.
Hence, the HCF = 2 × 2 × 3 = 12
ii) 15, 25 and 39
Solution:
Finding the prime factors of 15,25 and 30, we get
Hence, the common factor is 5.
Hence, the HCF = 5
iii) 8 and 12
Solution:
Finding the prime factors of 8 and 12, we get
Here the common factor is 2 (occurring twice)
Hence, the HCF = 2 × 2 = 4
iv) 12, 16 and 28
Solution:
Finding the prime factors of 12,16 and 28, we get
Here common factors are 2(occurring twice)
Hence, the HCF 12, 16 and 28 = 2 × 2 = 4