Find the Missing Digit in 632▯: Divisible by 3 Challenge

Q: What if multiple answers give sums divisible by 3?

In a well-designed multiple choice question, only one option should work. If you find multiple correct answers, double-check your arithmetic - you might have made a calculation error!

Q: Does this method work for other numbers like 9?

Yes! The digit sum rule works for both 3 and 9. For 9, the digit sum must be divisible by 9. There are similar rules for 6 (even AND divisible by 3) and 11 (alternating digit sum).

Q: What if the missing digit is in the middle of the number?

The position doesn't matter! Whether it's $ 6_32 $ or $ _632 $ or $ 632_ $, you still add all the digits the same way. The divisibility rule treats all digit positions equally.

Divisibility Rules with Missing Digit Problems

Complete the number so that it is divisible by 3 without a remainder:

$632▯$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's find the missing digit so the number can be divided by 3.

00:12 A number can be divided by 3 if the sum of its digits is also divisible by 3.

00:18 We will try different numbers, add them up, and see which makes the sum divisible by 3.

01:33 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the number so that it is divisible by 3 without a remainder:

$632▯$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Calculate the sum of the known digits $6 + 3 + 2 = 11$ .
Step 2: Consider each choice for the missing digit and calculate the new sum:
- $▯ = 9 : \quad 11 + 9 = 20$ (not divisible by 3)
- $▯=8:\quad11+8=19$ (not divisible by 3)
- $▯=7:\quad11+7=18$ (divisible by 3)
- $▯=5:\quad11+5=16$ (not divisible by 3)

Check which sum is divisible by 3. The sum of 18 (when ▯ is replaced by 7) is divisible by 3.

Hence, the choice $\boxed{7}$ completes the number so it is divisible by 3 without a remainder.

Therefore, the correct digit to complete the number is $7$ .

Final Answer

$7$

Key Points to Remember

Essential concepts to master this topic

Rule: A number is divisible by 3 if its digits sum to a multiple of 3
Technique: Sum known digits first: $6 + 3 + 2 = 11$ , then test each option
Check: Verify sum is divisible by 3: $11 + 7 = 18$ , and $18 ÷ 3 = 6$ ✓

Common Mistakes

Avoid these frequent errors

Testing divisibility by dividing the entire number instead of using digit sum
Don't try to divide 6327 by 3 directly = unnecessarily complicated calculation! This wastes time and increases chances for arithmetic errors. Always use the digit sum rule: add all digits and check if that sum divides by 3.

Practice Quiz

Test your knowledge with interactive questions

Determine if the following number is divisible by 3:

$$ 352 $$

FAQ

Everything you need to know about this question

Why does adding digits work for divisibility by 3?

This works because of how our number system is built! When you write a number like 632_, each digit represents powers of 10, and every power of 10 leaves remainder 1 when divided by 3. So the remainder of the whole number equals the remainder of the digit sum.

What if multiple answers give sums divisible by 3?

In a well-designed multiple choice question, only one option should work. If you find multiple correct answers, double-check your arithmetic - you might have made a calculation error!

Do I need to memorize multiples of 3?

Not necessarily! You can always divide by 3 to check. But knowing common multiples like 3, 6, 9, 12, 15, 18, 21 makes the process much faster.

Does this method work for other numbers like 9?

Yes! The digit sum rule works for both 3 and 9. For 9, the digit sum must be divisible by 9. There are similar rules for 6 (even AND divisible by 3) and 11 (alternating digit sum).

What if the missing digit is in the middle of the number?

The position doesn't matter! Whether it's $6_32$ or $_632$ or $632_$ , you still add all the digits the same way. The divisibility rule treats all digit positions equally.

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