Ex 3.4 Question 1.
Find the common factors of:
(a) 20 and 28
(b) 15 and 25
(c) 35 and 50
(d) 56 and 120
Solution:
(a) 20 and 28
Factors of 20 =1, 2, 4, 5, 10, 20
Factors of 28 = 1, 2, 4, 7, 28
Hence, the common factors =1, 2, and 4.
(b) 15 and 25
Factors of 15 =1, 3, 5, 15
Factors of 25 = 1, 5, 25
Hence, the common factors = 1 and 5.
(c) 35 and 50
Factors of 35 = 1, 5, 7, 35
Factors of 50 = 1, 2, 5, 10, 50
Hence, the common factors = 1 and 5.
(d) 56 and 120
Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
Factors of 120 =1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 30, 40, 60, 120
Hence, the common factors =1,2, 4, and 8.
Ex 3.4 Question 2.
Find the common factors of:
(a) 4, 8 and 12
(b) 5, 15 and 25
(6) 8 9484
Solution:
(a) 4, 8 and 12
Factors of 4 =1, 2, 4
Factors of 8 = 1, 2, 4, 8
Factors of 12 = 1, 2, 3, 4, 6, 12
Hence, the common factors = 1, 2, and 4.
(b) 5, 15 and 25
Factors of 5 = 1, 5
Factors of 15 = 1, 3, 5, 15
Factors of 25 = 1, 5, 25
Hence, the common factors = 1 and 5.
Ex 3.4 Question 3.
Find the first three multiples of:
(a) 6 and 8
(b) 12 and 18
Solution:
(a) 6 and 8
Multiple of 6 = 6, 12, 18, 24, 30, 36 , 42 , 48 , 54 , 60 , 66 , 72…………….
Multiple of 8 = 8 , 16 , 24 , 32 , 40 , 48 , 56 , 64 , 72 , 80………………………
First three common multiples of 6 and 8 = 24, 48, 72.
(b) 12 and 18.
Multiples of 12 =12 , 24 , 36 , 48 , 60 , 72 , 84 , 96 , 108 , 120……………………….
Multiples of 18 = 18 , 36 , 54 , 72 , 90 , 108…………………………….
First three common multiples of 12 and 18 = 36, 72, 108.
Ex 3.4 Question 4.
Write all the numbers less than 100 which are common multiples of 3 and 4.
Solution:
Multiple of 3 =
Common multiples of 3 and 4 less than 100= 12, 24, 36, 48, 60, 72, 84, and 96.
Ex 3.4 Question 5.
Which of the following numbers are co-prime?
(a) 18 and 35
(b) 15 and 37
(c) 30 and 415
(d) 17 and 68
(e) 216 and 215
(f) 81 and 16
Solution:
(a) 18 and 35
Factors of 18 = 1, 2, 3, 6, 9, 18
Factors of 35 = 1, 5, 7, 35
Common factors of 18 and 35 = 1.
Hence, 18 and 35 are co-prime.
(b) 15 and 37
Factors of 15= 1, 3, 5, 15
Factors of 37 = 1,37
The common factor of 15 and 37 = 1.
Hence, 15 and 37 are co-prime.
(c) 30 and 415
Factors of 30 = 1, 2, 3, 5, 6, 15, 30
Factors of 415 = 1, 5, 83
Common factors of 30 and 415 = 1 and 5
Hence, 30 and 415 are not co-prime.
(d) 17 and 68
Factors of 17 = 1, 17
Factors of 68 = 1, 2, 4, 17, 34, 68
Common factors of 17 and 68 = 1 and 17
Hence, 17 and 68 are not co-prime.
(e) 216 and 215
Factors of 216 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 54, 72, 108, 216
Factors of 215 = 1, 5, 43
Common factor of 216 and 215 = 1
Hence, 216 and 215 are co-prime.
(f) 81 and 16
Factors of 81 = 1, 3, 9, 27, 81
Factors of 16 = 1, 2, 4, 8, 16
Common to 81 and 16 = 1
Hence, 81 and 16 are co-prime.
Ex 3.4 Question 6.
A number is divisible by both 5 and 12. By which other will that number be always divisible?
Solution:
5 x 12 = 60.
Hence, the number must be divisible by 60.
Ex 3.4 Question 7.
A number is divisible by 12. By what other will that number be divisible?
Solution:
Factors of 12 = 1, 2, 3, 4, 6, 12
Hence the number also be divisible by= 1, 2, 3, 4, 6 and 12.
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