Playing with Numbers
Exercise 3.4
1). Find the common factors of :
(a) 20 and 28
Factors of 20 = 1, 2, 4, 5, 10, 20
Factors of 28 = 1, 2, 4, 7, 14, 28
Common factors = 1, 2, 4
(b) 15 and 25
Factors of 15 = 1, 3, 5, 15
Factors of 25 = 1, 5, 25
Common factors = 1, 5
(c) 35 and 50
Factors of 35 = 1, 5, 7, 35
Factors of 50 = 1, 2, 5, 10, 25, 50
Common factors = 1, 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, 22, 30, 40, 60,
120
Common factors = 1, 2, 4, 8
2). Find the common factors of :
(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
Common factors = 1, 2, 4
(b) 5, 15 and 25
Factors of 5 = 1, 5
Factors of 15 = 1, 3, 5, 15
Factors of 25 = 1, 5, 25
Common factors = 1, 5
3). Find first three common multiples of :
(a) 6 and 8
Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84,
90, 96, 102, . . . . . .
Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104,
112, 120, . . . . . . .
First three common multiples are = 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, 126, 144, 162, 180, . . .
First, three common multiples are = 36, 72, 108
4). Write all the numbers less than 100 which are common multiples of 3 and 4.
To find the common multiples of 3 and 4 we multiply 3 and 4
3 X 4 = 12
Multiples of 12 are = 12, 24, 36, 48, 60, 72, 84, 96
Therefore, common multiples of 3 and 4 less than 100 = 12, 24,
36, 48, 60, 72, 84, 96
5). Which of the following numbers are co-prime?
(a) 18 and 35
Factors of 18 = 1, 2, 3, 6, 9, 18
Factors of 35 = 1, 5, 7, 35
Common factors= 1
Therefore, 18 and 35 are co-prime numbers.
(b) 15 and 37
Factors of 15 = 1, 3, 5, 15
Factors of 37 = 1, 37
Common factors= 1
Therefore, 15 and 37 are co-prime numbers.
(c) 30 and 415
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Factors of 415 = 1, 5, 83, 415
Common factors= 1 , 5
Therefore, 30 and 415 are not co-prime numbers.
(d) 17 and 68
Factors of 17 = 1, 17
Factors of 68 = 1, 2 , 4, 17, 34, 68
Common factors= 1, 17
Therefore, 17 and 68 are not co-prime numbers.
(e) 216 and 215
Factors of 216 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108,
216
Factors of 215 = 1, 5, 43, 215
Common factors= 1
Therefore, 216 and 215 are co-prime numbers.
(f) 81 and 16
Factors of 81 = 1, 3, 9, 27, 81
Factors of 16 = 1, 2, 4, 8, 16
Common factors= 1
Therefore, 81 and 16 are co-prime numbers.
6). A number is divisible by both 5 and 12. By which other numbers will that number be always divisible?
If a number is divisible by both 5 and 12 then the number is multiple of 5 X 12 = 60.
The other number that divides the multiples of 60 are 2, 3, 4, 6.
(factors of 5 and 12)
7). A number is divisible by 12. By what other numbers will that number be divisible?
If a number is divisible by 12, then it is also divisible by the factors of 12 that are 2, 3, 4, 6.
