Detailed Solution for Divisibility Check

The question asks us to determine which of the given numbers (13, 9, 11, 4) is a divisor of the number 7918378. We can check this using the divisibility rules for each number.

Checking Divisibility by 4

Rule: A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

• The last two digits of 7918378 are 78.
• We check if 78 is divisible by 4: $78 \div 4 = 19.5$.
• Since 78 is not divisible by 4, the number 7918378 is not divisible by 4.

Checking Divisibility by 9

Rule: A number is divisible by 9 if the sum of its digits is divisible by 9.

• Sum of the digits of 7918378: $7 + 9 + 1 + 8 + 3 + 7 + 8 = 43$.
• We check if 43 is divisible by 9: $43 \div 9 = 4$ with a remainder of 7.
• Since the sum of the digits (43) is not divisible by 9, the number 7918378 is not divisible by 9.

Checking Divisibility by 11

Rule: A number is divisible by 11 if the difference between the sum of digits at odd places and the sum of digits at even places (counted from right to left or left to right) is either 0 or divisible by 11.

• Digits at odd places (1st, 3rd, 5th, 7th): 7, 1, 3, 8. Sum = $7 + 1 + 3 + 8 = 19$.
• Digits at even places (2nd, 4th, 6th, 8th): 9, 8, 7. Sum = $9 + 8 + 7 = 24$.
• Difference = $|19 - 24| = |-5| = 5$.
• Since the difference (5) is neither 0 nor divisible by 11, the number 7918378 is not divisible by 11.

Checking Divisibility by 13

Method: For divisibility by 13, we often use direct division or a more complex rule. Let's use direct division.

• We divide 7918378 by 13.
• Calculation: $7918378 \div 13 = 609106$.
• Since the division results in a whole number (an integer quotient with no remainder), the number 7918378 is divisible by 13.

Conclusion

Based on the checks:

• 7918378 is NOT divisible by 4.
• 7918378 is NOT divisible by 9.
• 7918378 is NOT divisible by 11.
• 7918378 IS divisible by 13.

Therefore, the number 7918378 is divisible by 13.