Determine if the following number is divisible by 3:
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Determine if the following number is divisible by 3:
To determine if the number 564 is divisible by 3, we apply the divisibility rule for 3:
Let's calculate the sum of the digits of 564:
Next, we check if 15 is divisible by 3. Since 15 can be divided by 3 without a remainder, it is divisible by 3:
Therefore, based on the divisibility rule, 564 is divisible by 3.
Thus, the correct answer is Yes.
Yes
Will a number divisible by 6 necessarily be divisible by 3?
This works because of how our base-10 number system interacts with multiples of 3. The mathematical proof involves modular arithmetic, but the rule always works reliably!
Keep adding! For example, if digits sum to 27, add again: . Since 9 is divisible by 3, so is the original number. Keep going until you get a single digit.
Yes! The digit sum rule works for both 3 and 9. If the digit sum is divisible by 9, then the original number is divisible by 9 (and automatically by 3 too).
Absolutely! The digit sum test is faster than long division and is a standard mathematical method. Teachers expect you to know and use divisibility rules efficiently.
Double-check your digit addition! Write it out clearly: , then . Small arithmetic errors will give you the wrong answer.
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