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Which of the following numbers is divisible by 12?
5642
7896
4322
9874
7896
A number is divisible by 12 if it is divisible by both 3 (sum of digits rule) and 4 (last two digits divisible by 4). Eliminate options not ending in a multiple of 4 first.
A set of four numbers: 5642, 7896, 4322, 9874. We need to identify which one is divisible by 12.
n=3├Ч4
A number is divisible by 12 if it is divisible by both 3 (sum of digits rule) and 4 (last two digits divisible by 4). Eliminate options not ending in a multiple of 4 first.
Many students check only for divisibility by 3 or only for divisibility by 4, leading to false positives.
Applying Divisibility by 4
For a number to be divisible by 12, it must be divisible by 4. A number is divisible by 4 if its last two digits form a number divisible by 4. Checking: 5642 (42/4=no), 7896 (96/4=yes), 4322 (22/4=no), 9874 (74/4=no).
96├╖4=24
Verifying Divisibility by 3
Since 7896 is the only option satisfying the divisibility rule for 4, we verify the sum of its digits for divisibility by 3. Sum = 7+8+9+6=30.
30├╖3=10
Conclusion
Since 7896 is divisible by both 3 and 4, it is divisible by 12.
7896├╖12=658
B is correct because 7896 is the only number among the choices that is divisible by both 3 and 4.
Understanding divisibility rules for composite numbers like 12, 18, or 72 is vital for fast arithmetic in simplification problems and LCM/HCF questions.
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