Page 46 - Maths Skill - 6

44 Maths

Solution: (i) We know that a number is divisible by 2, if its ones place digit is divisible by 2 or it is 0. Hence,
its ones place digit must be 0, 2, 4, 6 or 8. Therefore, the smallest digit to replace * in the given
number is 0.
(ii) We know that a number is divisible by 3 only if the sum of its digits is divisible by 3.
Here, 2 + 6 + 7 + 8 + 9 = 32, if we add the least number 1, the sum (32 + 1) 33 is divisible by
3. Hence, the required smallest digit is 1.
(iii) We know that a number is divisible by 5, only if its ones digit is either 0 or 5. Hence, 0 is the
smallest digit for the required place in the given number.

(iv) We know that a number is divisible by 8, only if the number formed by its last three digits
is divisible by 8 or last three digits are zeros. Clearly, the smallest digit is 2 so that 152 is
divisible by 8.
(v) We know that a number is divisible by 9, only if the sum of its digits is divisible by 9.
Here, 9 + 3 + 7 + 5 + 2 = 26. Clearly, 1 is the required smallest digit so that 27 is divisible
by 9.
(vi) We know that a number is divisible by 11, if the difference of the sums of alternate digits is
either 0 or divisible by 11.
Here, we have (4 + 5 + * + 8) – (2 + 9 + 4) = 17 + * – 15 = 2 + *. Clearly, 9 is the required
number to make it divisible by 11.
Example 2: Which of the following numbers are prime?
(i) 191 (ii) 295 (iii) 367
Solution: (i) Here, 191 < 14 × 14.

By using divisibility test, we see that 191 is not divisible by 2, 3, 5, 7 and 11. Also 191 is not
divisible by 13. So, 191 is a prime number.

(ii) Here, 295 < 18 × 18.
295 is divisible by 5. So, 295 is not a prime number.

(iii) Here, 367 < 20 × 20.
By using divisibility test, we see that 367 is not divisible by 2, 3, 5, 7 and 11. Also it is not
divisible by 13, 17 and 19. So, 367 is a prime number.

Exercise 3.3

1. State which of the following statements are True or False.
(i) If a number is divisible by 4, it is also divisible by 2.
(ii) If a number is divisible by 3, it must be divisible by 6.
(iii) If a number is divisible by 9, it is also divisible by 3.
(iv) If a number is divisible by 3 and 5, it is also divisible by 15.
(v) The sum of two consecutive odd numbers is always divisible by 4.
(vi) If a number divides the sum of two numbers, then it exactly divides them separately.

(vii) If the ten’s digit of a number is an odd number and the one’s digit is 2 or 6, the number is divisible by 4.
2. State which of the following numbers are divisible by 3, 5, 6, 9, 10, 11.
(i) 756 (ii) 21335 (iii) 50391 (iv) 3522

(v) 8964 (vi) 100090 (vii) 103081 (viii) 20834