Well-designed AP 6th Class Maths Solutions Chapter 3 Playing with Numbers Exercise 3.4 offers step-by-step explanations to help students understand problem-solving strategies.
Playing with Numbers Class 6 Exercise 3.4 Solutions – 6th Class Maths 3.4 Exercise Solutions
Question 1.
Find the common factors of :
a) 20 and 28
Solution:
Given numbers are 20 and 28.
Factors of 20 = 1,2,4,5,10,20
[∵ 1 × 20 = 20; 2 × 10 = 20; 4 × 5 =20; 5 × 4 = 20]
Factors of 28 = 1,2,4,7,14,28
[∵ 1 × 28 = 28; 2 × 14 = 28; 4 × 7 = 28]
∴ Hence, the common factors of 20 and 28 are 1, 2 and 4.
b) 15 and 25.
Solution:
Given numbers are 15 and 25
Factors of 15 = 1,3,5,15
[∵ 1 × 15 = 15; 3 × 5 = 15]
Factors of 25 = 1,5,25
[∵ 1 × 25 = 25; 5 × 5 = 25]
∴ Hence, the common factors of 15 and 25 are 1 and 5 .
c) 35 and 50
Solution:
Given numbers are 35 and 50.
Factors of 35 = 1,5,7,35
[∵ 1 × 35 = 35; 5 × 7 = 35]
Factors of 50 = 1,2,5,10,25,50
[∵ 1 × 50 = 50; 2 × 25 = 50; 5 × 10 = 50]
∴ Hence, the common factors of 35 and 50 are 1 and 5.
d) 56 and 120
Solution:
Given numbers are 56 and 120.
Factors of 56 = 1,2,4,7,8,14,28,56
[∵ 1 × 56 = 56; 2 × 28 = 56; 7 × 8 = 56; 14 × 4 = 56]
Factors of 120 = 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
[∵ 1 × 120 = 120; 2 × 60 = 120;
3 × 40 = 120; 4 × 30 = 120 ;
5 × 24 = 120; 6 × 20 = 120 ;
8 × 15 = 120; 10 × 12 = 120]
∴ Hence, the common factors of 56 and 120 are 1, 2, 4 and 8.
Question 2.
Find the common factors of :
a) 4,8 and 12
Solution:
Given numbers are 4,8 and 12.
Factors of 4 = 1,2,4 [∵ 4 × 1 = 4; 2 × 2 = 4]
Factors of 8 = 1,2,4,8 [∵ 1 × 8 = 8; 2 × 4 = 8]
Factors of 12 = 1,2,3,4,6,12 [∵ 12 × 1 = 12; 6 × 2 = 12; 3 × 4 = 12]
∴ Hence, the common factors of 4,8 and 12 are 1,2 and 4.
b) 5, 15 and 25
Sol. Given numbers are 5, 15 and 25.
Factors of 5 = 1,5 [∵ 1 × 5 = 5]
Factors of 15 = 1,3,5,15
[∵ 1 × 15 = 15; 3 × 5 = 15]
Factors of 25 = 1, 5, 25
[∵ 25 × 1 = 25; 5 × 5 = 25]
∴ Hence, the common factors of 5, 15 and 25 are 1 and 5.
Question 3.
Find first three common multiples of:
a) 6 and 8
Solution:
Given numbers are 6 and 8
Multiples of 6 are 6,12,18,24,30,36,42,48,54,60,66,72.
[∵ 6 × 1=6 ; 6 × 2 = 12 ; 6 × 3 = 18;
6 × 4 = 24; 6 × 5 = 30; 6 × 6 = 36; 6 × 7 = 42;
6 × 8 = 48; 6 × 9 = 54; 6 × 10 = 60;
6 × 11 – 66; 6 × 12 = 721
Multiples of 8 are 8,16,24,32,40,48, 56, 64, 72.
[∵ 8 × 1 = 8; 8 × 2 = 16; 8 × 3 = 24;
8 × 4 = 32; 8 × 5 = 40; 8 × 6 = 48; 8 × 7 = 56;
8 × 8 = 64 ; 8 × 9 = 72]
∴ First three common multiples of 6 and 8 = 24,48,72.
b) 12 and 18
Solution:
Given numbers are-12 aud 18
Multiples of 12 are 12.24,36,48,60,72, 84, 96, 108
[∵ 12 × 1 = 12 ; 12 × 2 + 24; 12 × 3 = 36; 12 × 4 = 48; 12 × 5 = 60 ; 12 × 6 = 72; 12 × 7 = 82; 12 × 8=96 ; 12 × 9=108]
Multiples of 18 are 18,36,54,72,90,108
[∵ 18 × 1 = 18; 18 × 2 = 36 ; 18 × 3 = 54;
18 × 4 = 72; 18 × 5 = 90; 18 × 6 = 108;]
∴ First three common multiples of 12 and 18 = 36,72,96.
Question 4.
Write all the numbers less than 100 which are common multiples of 3 and 4 .
Solution:
Given numbers are 3 and 4
Multiples of 3 less than 100 are :
Hence, the common multiples of 3 and 4 less than 100 are: 12,24,36,48,60,72,84 and 96.
Question 5.
Which of the following numbers are co-prime?
a) 18 and 35
Solution:
Given numbers are 18 and 35.
Factors of 18 = 1,2,3,6,9,18 [∵ 1 × 18 = 18; 2 × 9 = 18; 3 × 6 = 18]
Factors of 35 = 1,5,7,35 [∵ 35 × 1 = 35; 7 × 5 = 35]
Since, the common factors of 18 and 35 is only 1.
Hence, 18 and 35 are co-prime.
b) 15 and 37
Solution:
Given numbers are 15 and 37.
Factors of 15 = 1,3,5,15
[∵ 1 × 15 = 15; 3 × 5 = 15]
Factors of 37 = 1,37 [∵ 1 × 37 = 37]
Since, the common factors of 15 and 37 is only 1.
Hence, they are co-prime.
c) 30 and 415
Solution:
Given numbers are 30 and 415.
Factors of 30 = 1,2,3,5,6,10,15,30
[∵ 1 × 30 = 30; 2 × 15 = 30; 3 × 10 = 30; 5 × 6 = 30]
Factors of 415 = 1,5,83,415
[∵ 83 × 5 = 415; 415 × 1 = 415]
Since, the numbers have common factors 1 and 5.
Hence, they are not co-prime.
d) 17 and 68
Solution:
Given numbers are 17 and 68.
Factors of 17 = 1, 17 [∵ 1 × 17 = 17]
Factors of 68 = 1,2,4,17,34,68
[∵ 68 × 1 = 68; 34 × 2 = 68; 17 × 4 = 68]
Since, the number have common factors 1 and 17.
Hence, they are not co-prime.
e) 216 and 215
Solution:
Given numbers are 216 and 215.
Factors of 216 = 1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216
[∵ 1 × 216 = 216: 2 × 108 = 216;
3 × 72 = 108; 4 × 54 = 216; 6 × 36 = 216;
8 × 27 = 216; 9 × 24 = 216; 12 × 18 = 216]
Factors of 215 = 1,5,43,215
[∵ 1 × 215 = 215; 5 × 43 = 215]
Since, only 1 is the common factor of 216 and 215.
Hence, they are co-prime.
f) 81 and 16
Solution:
Given numbers are 81 and 16.
Factors of 81 = 1,3,9,27,81
[∵ 1 × 81 = 81; 3 × 27 = 81; 9 × 9 = 81]
Factors of 16 = 1,2,4,8,16
[∵ 16 × 1 = 16; 8 × 2 = 16; 4 × 4 = 16]
Since, only 1 is the common factor of 81 and 16
Hence, they are co-prime.
Question 6.
A number is divisible by both 5 and 12. By which other number will that number be always divisible?
Solution:
If the number is divisible by both 5 and 12 this the number will also be divisible 5 × 12 i.e., 60.
Question 7.
A number is divisible by 12. By what other numbers will that number be divisible?
Solution:
Factors of 12 are 1,2,3,4,6,12.
Hence, the number which is divisible by 12 , will also be divisible by its factors.
i.e., 1,2,3,4,6 and 12.