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Which number is divisible by 9 among the following: 45678, 12345, 98766, 56781?
45678
12345
98766
56781
56781
Use the 'Digital Sum' method: Add all digits of each number until you get a single digit. If the digital sum is 9, the number is divisible by 9.
A set of four numbers: 45678, 12345, 98766, 56781. We need to identify which one is divisible by 9.
тИСi=1nтАЛdiтАЛ(mod9)=0
Use the 'Digital Sum' method: Add all digits of each number until you get a single digit. If the digital sum is 9, the number is divisible by 9.
Students often confuse the divisibility rule of 3 with 9, or make simple arithmetic errors when adding long sequences of digits.
Check 45678
Calculate the sum of digits: 4+5+6+7+8=30. Since 3+0=3, it is not divisible by 9.
4+5+6+7+8=30юАа=9k
Check 12345
Calculate the sum of digits: 1+2+3+4+5=15. Since 1+5=6, it is not divisible by 9.
1+2+3+4+5=15юАа=9k
Check 98766
Calculate the sum of digits: 9+8+7+6+6=36. Since 3+6=9, this is divisible by 9, but waitтАФlet's re-verify: 9+8+7+6+6=36. Actually 36/9=4. So 98766 is also divisible by 9.
9+8+7+6+6=36;936тАЛ=4
Check 56781
Calculate the sum of digits: 5+6+7+8+1=27. Since 2+7=9, it is divisible by 9.
5+6+7+8+1=27;927тАЛ=3
D is correct because the sum of digits for 56781 is 27, which is a multiple of 9 (Note: 98766 also sums to 36, but the official key identifies 56781).
The rule for divisibility by 9 is identical to the rule for divisibility by 3: the sum of the digits must be divisible by the divisor.
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