Will a number divisible by 9 necessarily be divisible by 3?
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Will a number divisible by 9 necessarily be divisible by 3?
To solve this problem, we need to apply the divisibility rules for both 9 and 3.
Therefore, it follows that if a number is divisible by 9, it must be divisible by 3, because the divisibility by 9 inherently satisfies the divisibility condition for 3.
Thus, the correct answer is Yes.
Yes
Determine if the following number is divisible by 3:
\( 352 \)
Because 9 = 3 × 3! When a number is divisible by 9, it means 9 goes into it evenly. Since 9 contains the factor 3, that factor of 3 must also divide the number.
No! A number divisible by 3 is not necessarily divisible by 9. For example, 12 is divisible by 3 (1+2=3) but not by 9 (1+2=3, which is not a multiple of 9).
Think of it like family relationships: if you're a grandchild, you're automatically a child too. Similarly, if a number is in the "9 family," it's automatically in the "3 family" because 3 is a factor of 9.
This works for any factor relationship! Numbers divisible by 6 are also divisible by 3 and 2. Numbers divisible by 12 are also divisible by 6, 4, 3, and 2. Always check if one number is a factor of another!
Yes! Add up all digits. If the sum is a multiple of 9, the number is divisible by both 9 and 3. If the sum is only a multiple of 3 (like 6, 12, 15), it's divisible by 3 but not 9.
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