Question 2 - Figure it out - Page 126 - Chapter 5 Class 8 - Number Play (Ganita Prakash)

Transcript

Question 2 Find the smallest multiple of 9 with no odd digits.So, we have two constraints (rules) Rule 1: No odd digits allowed. We can only use 0, 2, 4, 6, 8. Rule 2: Since number is a multiple of 9, it is divisible by 9. Thus, sum of the digits must be a multiple of 9. Since we are using only even digits, the number would be an even number And, Sum of digits would also be even (As Even + Even = Even) Now, Multiples of 9 are: 9, 18, 27, 36, 45,.. Since we need smallest number, we take smallest even multiple Thus, the smallest sum we can aim for is 18. To find the smallest number, we want the fewest digits possible. Taking 2 digit number We can use digits 0, 2, 4, 6, 8 The biggest even digits are 8 and 8 (8 + 8 = 16), which is not enough to reach 18. So, it must be a 3-digit number. Taking 3 digit number To make it the smallest, the first digit should be as small as possible. The smallest non-zero even digit is 2 So, first digit = 2. We need the other two digits to add up to 16 (because 18 - 2 = 16). The only way to get 16 using even single digits is 8 + 8. So the digits are 2, 8, 8. Thus, our smallest multiple is 288