If 7126 is divided by 48, find the remainder.

The correct answer is Option (1) → 1

Look for a small power of 7 that leaves remainder 1 when divided by 48; every higher power built from it then leaves remainder 1 too.

• \(7^{2}=49=48+1\), so \(7^{2}\) leaves remainder 1

• \(7^{126}=\left(7^{2}\right)^{63}\), a product of 63 numbers that each leave remainder 1

• So \(7^{126}\) leaves remainder \(1^{63}=1\)