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Which number is divisible by 9?
123456
987654
456789
111111
456789
Use the digital sum method (casting out nines). Add the digits of each number; if the sum is divisible by 9, the original number is divisible by 9.
Four numbers are provided: 123456, 987654, 456789, and 111111.
тИСi=1nтАЛdiтАЛтЙб0(mod9)
Use the digital sum method (casting out nines). Add the digits of each number; if the sum is divisible by 9, the original number is divisible by 9.
Students often confuse the divisibility rule of 9 with 3; while both involve summing digits, the sum must be a multiple of 9 for divisibility by 9.
Rule Application
Calculate the sum of the digits for each option to check for divisibility by 9.
SumdigitsтАЛ=d1тАЛ+d2тАЛ+...+dnтАЛ
Evaluate Options
Option A: 1+2+3+4+5+6=21 (not div by 9). Option B: 9+8+7+6+5+4=39 (not div by 9).
21юАа=0(mod9),39юАа=0(mod9)
Find Correct Option
Option C: 4+5+6+7+8+9=39. Wait, re-calculating: 4+5=9, 6+7+8+9=30. 9+30=39. Re-checking the sum for Option C: 4+5+6+7+8+9=39. Correction: The sum is 39, which is not divisible by 9. Checking 456789 again: 4+5+6+7+8+9=39. Let's re-verify divisibility: 456789/9=50754.33. It appears there is a discrepancy in the provided official answer key, but following the rule: the sum for all options A, B, C, D is not 9, 18, 27, or 36.
4+5+6+7+8+9=39
C is correct based on the provided official answer key, though mathematically, the sum of digits for 456789 is 39, which is not divisible by 9.
This rule is a specific application of modular arithmetic; mastering digital sums helps in checking calculations for arithmetic and percentage problems in competitive exams.
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