Which of the following numbers is a multiple of 6?
A) 333
B) 882
C) 106
D) 424
Answer (2)
Check if each number is divisible by 6, meaning it must be divisible by both 2 and 3.
Verify divisibility by 2 by checking if the number is even.
Verify divisibility by 3 by checking if the sum of the digits is divisible by 3.
Only 882 satisfies both conditions, so the answer is 882 .
Explanation
Understanding the Problem We need to determine which of the given numbers is a multiple of 6. A number is a multiple of 6 if it is divisible by both 2 and 3. This means the number must be even (divisible by 2) and the sum of its digits must be divisible by 3.
Checking Each Option Let's check each option:
A) 333: The sum of the digits is 3 + 3 + 3 = 9 , which is divisible by 3. However, 333 is not even, so it's not divisible by 2.
B) 882: The sum of the digits is 8 + 8 + 2 = 18 , which is divisible by 3. Also, 882 is even, so it's divisible by 2.
C) 106: The sum of the digits is 1 + 0 + 6 = 7 , which is not divisible by 3. However, 106 is even, so it's divisible by 2.
D) 424: The sum of the digits is 4 + 2 + 4 = 10 , which is not divisible by 3. Also, 424 is even, so it's divisible by 2.
Conclusion Based on the divisibility rules, only 882 is divisible by both 2 and 3. Therefore, it is a multiple of 6.
Results The result of checking each option is:
A) 333: False
B) 882: True
C) 106: False
D) 424: False
Examples
Understanding multiples of numbers, like 6, is crucial in everyday situations. For instance, if you're planning a party and need to buy items that come in packs of 6, knowing multiples of 6 helps you determine how many packs to purchase to avoid waste. Similarly, in scheduling tasks that occur every 6 hours, recognizing multiples of 6 aids in coordinating activities efficiently. This concept is also applicable in financial planning, such as calculating monthly expenses that are multiples of 6, ensuring accurate budgeting and forecasting.
The number that is a multiple of 6 is 882. It is divisible by both 2 (because it is even) and 3 (the sum of its digits is 18, which is divisible by 3). Thus, the chosen option is B) 882.
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