Complete the Number: Make 13? Divisible by 10

Q: Why can't 1, 2, or 3 work as the missing digit?

For divisibility by 10, the number must end in 0. Numbers ending in 1, 2, or 3 (like 131, 132, 133) will always have remainders when divided by 10.

Q: What if none of the answer choices seem right?

Sometimes 'All answers are incorrect' or 'None of the above' is the right choice! Don't force a wrong answer just because it's listed - trust your mathematical reasoning.

Q: Can I just divide each option to check?

Yes! You can test: $ 131 ÷ 10 = 13.1 $, $ 132 ÷ 10 = 13.2 $, $ 133 ÷ 10 = 13.3 $. All have remainders, confirming none work.

Q: Are there other numbers that work besides 0?

No! For divisibility by 10, only 0 works as the ones digit. This makes 130 the unique answer for $ 13? $.

Divisibility Rules with Missing Digits

Complete the number so that it is divisible by 10 without a remainder:

$13\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the digit so that the number is divisible by 10

00:03 A number divisible by 10 is a number with ones digit 0

00:08 Using this method, we will go through all numbers and eliminate accordingly

00:15 No digit is suitable, 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

Complete the number so that it is divisible by 10 without a remainder:

$13\text{?}$

Step-by-step solution

To determine the missing number that makes $13?$ divisible by 10, we must consider the divisibility rule for 10: A number is divisible by 10 if its last digit is 0. Therefore, for the number $13?$ to be divisible by 10, ? must be 0.

We examine the answer choices:

Choice 1: 1. If ? is 1, the number $131$ is not divisible by 10.
Choice 2: 2. If ? is 2, the number $132$ is not divisible by 10.
Choice 3: 3. If ? is 3, the number $133$ is not divisible by 10.
Choice 4: All answers are incorrect. The number should be $130$ to be divisible by 10.

Upon examining the choices, since none corresponds to a digit of 0, the correct answer is indicated by Choice 4: All answers are incorrect.

Final Answer

All answers are incorrect.

Key Points to Remember

Essential concepts to master this topic

Rule: A number is divisible by 10 only if it ends in 0
Technique: For 13?, the missing digit must be 0 to make 130
Check: Verify 130 ÷ 10 = 13 with no remainder ✓

Common Mistakes

Avoid these frequent errors

Choosing any digit from the given options
Don't pick from choices 1, 2, or 3 just because they're listed = wrong answer! These create 131, 132, 133 which aren't divisible by 10. Always apply the divisibility rule: only 0 in the ones place makes a number divisible by 10.

Practice Quiz

Test your knowledge with interactive questions

Is the number 43 divisible by 4?

FAQ

Everything you need to know about this question

Why can't 1, 2, or 3 work as the missing digit?

For divisibility by 10, the number must end in 0. Numbers ending in 1, 2, or 3 (like 131, 132, 133) will always have remainders when divided by 10.

How do I remember the divisibility rule for 10?

Think of counting by tens: 10, 20, 30, 40... Notice they all end in 0! Any number divisible by 10 must follow this pattern.

What if none of the answer choices seem right?

Sometimes 'All answers are incorrect' or 'None of the above' is the right choice! Don't force a wrong answer just because it's listed - trust your mathematical reasoning.

Can I just divide each option to check?

Yes! You can test: $131 ÷ 10 = 13.1$ , $132 ÷ 10 = 13.2$ , $133 ÷ 10 = 13.3$ . All have remainders, confirming none work.

Are there other numbers that work besides 0?

No! For divisibility by 10, only 0 works as the ones digit. This makes 130 the unique answer for $13?$ .

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