What is the remainder when the number \((44)^2\) is divided by 9?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1
The remainder of a product is the remainder of the product of the remainders. So the remainder of \(44\) on division by 9 is found first and then squared.
\(44=4\times9+8\), so 44 leaves remainder 8
\(8^2=64=7\times9+1\), so \((44)^2\) leaves remainder 1
Shortcut: 44 is one less than 45, a multiple of 9, so 44 leaves remainder \(-1\), and \((-1)^2=1\).