Concept used:

Divisibility of 11 – Difference between the sum of digits at odd and even places will be zero or multiple of 11.

Divisibility of 7 – Subtract the twice of unit digit from remaining number and check if Resultant number is divisible by 7

Calculation:

Divisibility of 11 – Difference between the sum of digits at odd and even places will be zero or multiple of 11.

Divisibility of 7 – Subtract the twice of unit digit from remaining number and check if Resultant number is divisible by 7

We firstly check the numbers divisible by 11, if it satisfies then we proceed to check the divisibility of 7

16425 : (5 + 4 + 1) – (2 + 6)

⇒ 10 – 8 = 2

Not equal to zero or multiple of 11, hence not divisible by 11.

12235 : (5 + 2 +1) – (3 + 2)

⇒ 9 – 5 = 4

4 is not equal to zero or multiple of 11, hence not divisible by 11

16257 : (6 + 5) - (7 + 2 + 1)

⇒ 11 – 10 = 1

1 is not equal to zero or multiple of 11, hence not divisible by 11

16324 : (4 + 3 + 1) – (2 + 6)

⇒ 8 – 8 = 0

Difference is equal to zero, hence divisible by 11

For this only we check divisibility of 7

1632 – (2 × 4)

⇒ 1632 – 8 = 1624

162 – (2 × 4)

⇒ 162 – 8 = 154

15 – (2 × 4)

⇒ 15 – 8 = 7

This number is also divisible by 7

∴ 16324 is divisible by both 7 and 11.