Question

Illustrative Examples
ample 1.
In each of the following numbers, replace the sign
*** by the smallest digit to make them
divisible by the given number:
(a) 308* by 2
(b) 267*89 by 3
(c) 45*8* by 5
(d) 56315* by 8
(e) 9375*2 by 9
(f) 4259*48 by 11
Jon : (a)
We know that a number is divisible by 2, if its one's place digit is divisible by 2 or it is
0. Hence, its one's place digit must be 0, 2, 4, 6 or 8. Therefore, the smallest digit to
replace * in the given number is 0.
(b)
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.
(c)
We know that a number is divisible by 5, only if its one's digit is either 0 or 5. Hence,
is the smallest digit for the required place in the given number.
(d)
We know that a number is divisible by 8, only if the number formed by its last th
digits is divisible by 8 or last three digits are zeros. Clearly, the smallest digit is:
that 152 is divisible by 8.
(e) We know thať a number is divisible by 9, only if the sum of its digits is divisible
Here, 9 +3+7+5+2 = 26. Clearly, 1 is the required smallest digit so that
divisible by 9.
(f) We know that a number is divisible by 11, if the difference of the sums of alt
digits is either 0 or divisible by 11.
Here, we have (4+5+* + 8) –(2+9+4)=17+* -15= 2+*. Clearly, 9 is ther
number to make it divisible by 11.टोका टोका डिजिटल समझ में नहीं आया है ​

Answer 1

Answer:

(a) o (b)1okkkkkkkkkkk