Page 37 - Maths Class 06

We conclude from the above table that:
(i) The multiples of any natural number is the 1, 2, 3, 4, 5,… multiplier.
(ii) The multiple of natural number are the natural number by which they are exactly divided.

(iii) The smallest multiple of a natural number is the number itself.
(iv) The biggest multiple of the natural number can not be defined.
(v) If the multi ple number ‘b’ is the factor of natu ral number ‘a’, then the number ‘a’ is the multi ple of
natu ral number ‘b’.

EX AM PLE 1. Write all the fac tors of:
(a) 20 (b) 25
SO LU TION : (a) We know that, (b) We know that,
20 = 1 × 20 25 = 1 25´
20 = 2 × 10 25 = 5 5´
20 = 4× 5 Thus, all factors of 25 are

Thus, all factors of 20 are 1, 5 and 25.
1, 2, 4, 5, 10 and 20.
EX AM PLE 2. Find the com mon fac tors of:
(a) 30 and 64 (b) 35 and 45 (c) 56 and 120

SO LU TION : (a) 30 and 64
All possible factors of 30 are 1 , 2 , 3, 5, 6, 10, 15 and 30.

All possible factors of 64 are 1 , 2 , 4, 8, 16, 32 and 64.
Therefore, common factors of 30 and 64 are 1 and 2.

(b) 35 and 45

All possible factors of 35 are 1 , 5 , 7 and 35.
All possible factors of 45 are 1 , 3, 5 , 9, 15 and 45.

Therefore, common factors of 35 and 45 are 1 and 5.
(c) 56 and 120

All possible factors of 56 are 1 , 2 , 4 , 7, 8 , 14, 28 and 56.
All possible factors of 120 are 1 , 2 , 3, 4 , 5, 6, 8 , 10, 12, 15, 20, 30, 40, 60

and 120.
Therefore, common factors of 56 and 120 are 1, 2, 4, and 8.
EX AM PLE 3. Write the first five mul ti ples of 5.

SO LU TION : First five mul ti ples of 5 are:
5 1 5´ = ; 5 2 10´ = ; 5 3´ = 15 ; 5 ´ 4 20= ; 5 5´ = 25

Thus, 5, 10, 15, 20 and 25 are first five multiples of 5.
EX AM PLE 4. Find the first three com mon mul ti ples of:
(a) 4 and 6 (b) 12 and 18.

37 Mathematics-6