Using divisibility tests, determine which of the following are divisible by 4: (a) 4096 (b) 21084 (c) 31795012
All three: (a), (b) and (c)
Rule for 4: A number is divisible by 4 if the last two digits form a number divisible by 4.
(a) 4096
Look at the last two digits: \(96\).
Check: \(96 \div 4 = 24\).
Since \(24\) is a whole number, \(96\) is divisible by 4.
Therefore, \(4096\) is divisible by 4.
(b) 21084
Look at the last two digits: \(84\).
Check: \(84 \div 4 = 21\).
Since \(21\) is a whole number, \(84\) is divisible by 4.
Therefore, \(21084\) is divisible by 4.
(c) 31795012
Look at the last two digits: \(12\).
Check: \(12 \div 4 = 3\).
Since \(3\) is a whole number, \(12\) is divisible by 4.
Therefore, \(31795012\) is divisible by 4.
Conclusion: All three numbers are divisible by 4.