Divisibility Test: Is 132 Divisible by 3?

Q: Why does adding digits tell us if a number is divisible by 3?

This works because of how our base-10 number system relates to multiples of 3. The mathematical proof involves modular arithmetic, but the rule always works! Trust the pattern - it's been proven mathematically.

Q: Does this work for bigger numbers like 1,234,567?

Yes! Add all digits: $ 1+2+3+4+5+6+7 = 28 $, then $ 2+8 = 10 $. Since 10 is not divisible by 3, neither is 1,234,567.

Q: Can I use this method for divisibility by other numbers?

The digit sum method works for 3 and 9 only. For other numbers like 2, 4, 5, 6, 8, you need different divisibility rules. Each number has its own special pattern!

Q: What if I make a mistake adding the digits?

Double-check your addition! Write it out: 132 → 1 + 3 + 2 = 6. If you're unsure, you can always verify by doing the actual division as a final check.

Divisibility Rules with Digit Sum Method

Determine if the following number is divisible by 3:

$132$

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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

00:04 A number is divisible by 3 only if the sum of its digits is divisible by 3

00:09 Let's sum its digits and divide by 3

00:14 The sum of digits is divisible by 3, therefore the number is 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

Understand the problem

Determine if the following number is divisible by 3:

$132$

Step-by-step solution

To determine if the number $132$ is divisible by $3$ , we can apply the rule for divisibility by $3$ , which involves summing the digits of the number.

Step-by-step solution:

Step 1: Sum the digits of the number $132$ .
$1 + 3 + 2 = 6$
Step 2: Check if the sum is divisible by $3$ .
$6 \div 3 = 2$ , which is an integer.

Since the sum of the digits is $6$ and $6$ is divisible by $3$ , the number $132$ is also divisible by $3$ .

Therefore, the number $132$ is divisible by $3$ , and the correct choice is:

Yes

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Rule: A number is divisible by 3 if its digit sum is divisible by 3
Technique: Add all digits: $1 + 3 + 2 = 6$ , then check if 6 ÷ 3 = 2
Check: Verify by actual division: $132 ÷ 3 = 44$ with no remainder ✓

Common Mistakes

Avoid these frequent errors

Testing divisibility by dividing the original number instead of using digit sum
Don't calculate 132 ÷ 3 = 44 to check divisibility! While this works, it defeats the purpose of the quick digit sum rule. Always add the digits first (1 + 3 + 2 = 6), then 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 tell us if a number is divisible by 3?

This works because of how our base-10 number system relates to multiples of 3. The mathematical proof involves modular arithmetic, but the rule always works! Trust the pattern - it's been proven mathematically.

What if the digit sum is a large number?

Keep adding digits until you get a single digit! For example, if digits sum to 15, then $1 + 5 = 6$ . Since 6 is divisible by 3, the original number is too.

Does this work for bigger numbers like 1,234,567?

Yes! Add all digits: $1+2+3+4+5+6+7 = 28$ , then $2+8 = 10$ . Since 10 is not divisible by 3, neither is 1,234,567.

Can I use this method for divisibility by other numbers?

The digit sum method works for 3 and 9 only. For other numbers like 2, 4, 5, 6, 8, you need different divisibility rules. Each number has its own special pattern!

What if I make a mistake adding the digits?

Double-check your addition! Write it out: 132 → 1 + 3 + 2 = 6. If you're unsure, you can always verify by doing the actual division as a final check.

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Divisibility Test: Is 132 Divisible by 3?

Divisibility Rules with Digit Sum Method

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why does adding digits tell us if a number is divisible by 3?

What if the digit sum is a large number?

Does this work for bigger numbers like 1,234,567?

Can I use this method for divisibility by other numbers?

What if I make a mistake adding the digits?

🌟 Unlock Your Math Potential

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