The number 7918378 is divisible by:
- A13
- B9
- C11
- D4
Solution & Step-by-step Explanation
Let's check each option using divisibility rules:
Divisibility by 4: The last two digits must be divisible by 4. Here, the last two digits are 78. Since 78÷4=19.5, it is not divisible by 4.
Divisibility by 9: The sum of the digits must be a multiple of 9.
Sum=7+9+1+8+3+7+8=43
Since 43 is not a multiple of 9, it is not divisible by 9.
Divisibility by 11: The difference between the sum of digits at odd places and even places must be 0 or a multiple of 11.
Sum of odd positions (from right)=8+3+1+7=19
Sum of even positions (from right)=7+8+9=24
Difference=24−19=5
Since 5 is not a multiple of 11, it is not divisible by 11.
Divisibility by 13: Let's perform direct division:
7918378÷13=609106
Since it leaves a remainder of 0, the number is exactly divisible by 13.
Divisibility by 4: The last two digits must be divisible by 4. Here, the last two digits are 78. Since 78÷4=19.5, it is not divisible by 4.
Divisibility by 9: The sum of the digits must be a multiple of 9.
Sum=7+9+1+8+3+7+8=43
Since 43 is not a multiple of 9, it is not divisible by 9.
Divisibility by 11: The difference between the sum of digits at odd places and even places must be 0 or a multiple of 11.
Sum of odd positions (from right)=8+3+1+7=19
Sum of even positions (from right)=7+8+9=24
Difference=24−19=5
Since 5 is not a multiple of 11, it is not divisible by 11.
Divisibility by 13: Let's perform direct division:
7918378÷13=609106
Since it leaves a remainder of 0, the number is exactly divisible by 13.