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प्रश्न
If 31z5 is a multiple of 9, where z is a digit, what is the value of z? You will find that there are two answers for the last problem. Why is this so?
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उत्तर
If a number is a multiple of 9, then the sum of its digits will be divisible by 9.
Sum of digits of 31z5 = 3 + 1 + z + 5 = 9 + z
Hence, 9 + z should be a multiple of 9.
This is possible when 9 + z is any one of these numbers 0, 9, 18, 27, and so on …
However, since z is a single digit number, this sum can be either 9 or 18. Therefore, z should be either 0 or 9.
संबंधित प्रश्न
If 24x is a multiple of 3, where x is a digit, what is the value of x?
(Since 24x is a multiple of 3, its sum of digits 6 + x is a multiple of 3; so 6 + x is one of these numbers: 0, 3, 6, 9, 12, 15, 18…. But since x is a digit, it can only be that 6 + x = 6 or 9 or 12 or 15. Therefore, x = 0 or 3 or 6 or 9. Thus, x can have any of four different values)
If x is a digit such that the number \[\overline{{18x71}}\] is divisible by 3, find possible values of x.
Find the remainder when 51439786 is divided by 3. Do this without performing actual division.
Which of the following statement is true?
If a number is divisible by 9, it must be divisible by 3.
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Find which of the following numbers are divisible by 3:
(i) 261
(ii) 777
(iii) 6657
(iv) 2574
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Find A as required:
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Let abc be a three-digit number. Then abc – cba is not divisible by ______.
Why is 872 NOT divisible by 3?
