Divisibility Test: Is 352 Divisible by 3?

Divisibility Rules with Sum of Digits

Determine if the following number is divisible by 3:

352 352

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine if the number is divisible by 3
00:03 A number is divisible by 3 only if the sum of its digits is divisible by 3
00:08 Let's sum its digits and divide by 3
00:15 The sum of digits is not divisible by 3, therefore the number is not divisible by 3
00:18 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Determine if the following number is divisible by 3:

352 352

2

Step-by-step solution

To determine if 352 is divisible by 3, we need to follow these steps:

  • Calculate the sum of its digits.
  • Check if this sum is divisible by 3.

Let's work through the procedure:

The number 352 352 consists of the digits 3, 5, and 2.

Step 1: Calculate the sum of the digits.

The sum is 3+5+2=10 3 + 5 + 2 = 10 .

Step 2: Check if 10 is divisible by 3.

Since 10 divided by 3 gives a remainder, 10 is not divisible by 3.

Therefore, the number 352 is not divisible by 3.

The correct answer is No.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Rule: A number is divisible by 3 if sum of digits is divisible by 3
  • Technique: For 352: add 3 + 5 + 2 = 10, then check if 10 ÷ 3
  • Check: Since 10 ÷ 3 = 3 remainder 1, the sum fails the test ✓

Common Mistakes

Avoid these frequent errors
  • Dividing the original number instead of checking digit sum
    Don't divide 352 ÷ 3 = 117.33... to check divisibility! This takes longer and you might make calculation errors. Always add the digits first: 3 + 5 + 2 = 10, then check if 10 is divisible 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 to test divisibility by 3?

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This works because of how our place value system relates to multiples of 3. When you break down any number into its digits, the leftover parts after removing multiples of 3 will always equal the digit sum modulo 3.

What if the digit sum is still a large number?

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Keep adding! For example, if digit sum = 27, add again: 2 + 7 = 9. Since 9 is divisible by 3, the original number is too. Keep going until you get a single digit.

Does this trick work for other numbers besides 3?

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Yes! The digit sum test works for 3 and 9. For other numbers like 2, 4, 5, 6, 8, and 10, you need different rules (like checking the last digit or last few digits).

How can I quickly tell if 10 is divisible by 3?

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Think of multiples of 3: 3, 6, 9, 12... Since 10 falls between 9 and 12, it's not a multiple of 3. You can also do 10 ÷ 3 = 3 remainder 1.

What if I make an error adding the digits?

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Double-check your addition! For 352: write it out clearly as 3 + 5 + 2. Count on your fingers if needed. Accuracy in the digit sum is crucial for the right answer.

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