Which number is divisible by both 5 and 6?
A) 132,359
B) 142,645
C) 164,780
D) 193,560
Answer (2)
The number that is divisible by both 5 and 6 from the given options is 193,560. It meets the criteria for divisibility by being even and having a digit sum that is divisible by 3. Thus, the answer is option D: 193,560.
;
Check if the number ends with 0 or 5 to be divisible by 5.
Check if the number is even and the sum of its digits is divisible by 3 to be divisible by 6.
Test each option to see if it meets both criteria.
The number that satisfies both conditions is 193 , 560 .
Explanation
Problem Analysis We need to find a number from the given options that is divisible by both 5 and 6. A number divisible by 5 must end in 0 or 5. A number divisible by 6 must be divisible by both 2 and 3, meaning it must be even and the sum of its digits must be divisible by 3.
Checking Each Option Let's check each option:
Option A: 132,359. This number ends in 9, so it is not divisible by 5. Therefore, it cannot be divisible by both 5 and 6.
Option B: 142,645. This number ends in 5, so it is divisible by 5. Let's check the sum of its digits: 1 + 4 + 2 + 6 + 4 + 5 = 22 . Since 22 is not divisible by 3, the number 142,645 is not divisible by 3, and therefore not divisible by 6.
Option C: 164,780. This number ends in 0, so it is divisible by 5. Let's check the sum of its digits: 1 + 6 + 4 + 7 + 8 + 0 = 26 . Since 26 is not divisible by 3, the number 164,780 is not divisible by 3, and therefore not divisible by 6.
Option D: 193,560. This number ends in 0, so it is divisible by 5. Let's check the sum of its digits: 1 + 9 + 3 + 5 + 6 + 0 = 24 . Since 24 is divisible by 3, and the number is even, it is divisible by 6.
Conclusion Therefore, the number 193,560 is divisible by both 5 and 6.
Examples
Understanding divisibility rules is useful in many real-life situations. For example, if you are distributing items equally among a group of people, knowing divisibility rules can help you quickly determine if the items can be divided evenly. If you have 30 items and want to divide them among 6 people, you can use the divisibility rule of 6 to quickly see that 30 is divisible by 6, so each person can receive 5 items without any leftovers. This concept is also useful in financial calculations, such as determining if a loan payment can be made in equal monthly installments.
