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What is the smallest number, which when multiplied by 9 gives the product having the digit 5 only in all places ?
Explanation
To find the smallest number, we identify the smallest product consisting only of the digit 5 that is divisible by 9. According to the divisibility rule for 9, a number is divisible by 9 if the sum of its digits is a multiple of 9.
If the product consists of n digits of 5, the sum of its digits is 5 × n. For 5n to be divisible by 9, n must be a multiple of 9 (since 5 and 9 are coprime). The smallest such value for n is 9.
Therefore, the smallest product is 555,555,555. To find the required number, we divide this product by 9:
555,555,555 ÷ 9 = 61,728,395
Thus, 61,728,395 is the smallest number that, when multiplied by 9, results in a product containing only the digit 5 in all places.
SIMILAR QUESTIONS
Which one of the following is the largest 3-digit number which when divided by 12, 15 and 18 respectively, gives a remainder 5 in each case ?
3 digits are chosen at random from 1, 2, 3, 4, 5, 6, 7, 8 and 9 without repeating any digit. What is the probability that their product is odd?
A is the smallest positive integer which when divided by 9 and 12 leaves remainder 8. B is the smallest positive integer which when divided by 9 and 12 leaves remainder 5. Which one of the following is the value of A - B ?
What is the greatest number less than 1000 which when divided respectively by 5, 7 and 9 leaves the remainders 3, 5 and 7 respectively ?