Question

When a number is divided by 11, it gives a remainder of 9. What will be the remainder if the square of that number is divided by 11?​

Answer 1

As we know that , when we multiply the divisor with quotient and then by adding the remainder in them we get the dividend .

➛ [ Divisor × Quotient ] + Reminder = Dividend

Let any number as the Quotient ( 1, 2, 3, 4, 5,6....... so on )

According to the question :

➛ When a number is divided by 11, it gives a remainder of 9.

• Let the number (Dividend) be x and choosing a quotient 5 .

➛ ( 11 × 5 ) + 9 = x

➛ 55 + 9 = x

➛ 64 = x

Square of 64 = 4096

• ( dividing 4096 by 11 )

➛ 11 ❫ 4096 ❪ 372

33

✗79

77

✗26

22

✗4

• Let the number (Dividend) be x and choosing a quotient 2 .

➛ ( 11 × 2 ) + 9 = x

➛ ( 11 × 2 ) + 9 = x➛ 22 + 9 = x

➛ ( 11 × 2 ) + 9 = x➛ 22 + 9 = x➛ 31 = x

Square of 31 = 961

• ( dividing 961 by 11 )

➛ 11 ❫ 961 ❪ 87

88

✗81

77

✗4

• Let the number (Dividend) be x and choosing a quotient 10 .

➛ ( 11 × 10 ) + 9 = x

➛ ( 11 × 10 ) + 9 = x➛ 110 + 9 = x

➛ ( 11 × 10 ) + 9 = x➛ 110 + 9 = x➛ 119 = x

Square of 119 = 14161

• Square of 119 = 14161( dividing 14161 by 11 )

➛ 11 ❫ 14161 ❪ 1287

11

✗31

22

✗96

88

✗81

77

✗4

So, if we divide the square of that number by 11 the remainder will become 4 .