Will a number divisible by 9 necessarily be divisible by 6?
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Will a number divisible by 9 necessarily be divisible by 6?
To determine if a number divisible by 9 is necessarily divisible by 6, let's explore the divisibility rules.
A number is divisible by 9 if the sum of its digits is divisible by 9. Consequently, such a number is also divisible by 3 since divisibility by 9 implies divisibility by 3.
For divisibility by 6, a number must be divisible by both 2 and 3. We've established that a number divisible by 9 is also divisible by 3, so we now need to check whether it is necessarily divisible by 2.
Consider an example: the number 27 is divisible by 9 since , which is divisible by 9. However, 27 is odd (since ), and thus, not divisible by 2.
Since 27 is not divisible by both 2 and 3, this number is not divisible by 6.
Therefore, a number divisible by 9 is not necessarily divisible by 6. The correct answer is No.
No
Determine if the following number is divisible by 3:
\( 352 \)
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