Divisibility Challenge: Find Missing Digits for 51— to Be Divisible by 10

Q: Why must the last digit be 0 for divisibility by 10?

Because 10 = 2 × 5, a number must be divisible by both 2 and 5. Only numbers ending in 0 satisfy both conditions - they're even (divisible by 2) and end in 0 or 5 (divisible by 5).

Q: Can the first missing digit be any number?

Yes! Since we need $ 51_0 $, the third digit can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. All would make valid numbers divisible by 10.

Q: How do I quickly check if a number is divisible by 10?

Simply look at the last digit! If it's 0, the entire number is divisible by 10. No calculation needed - it's that easy!

Q: Why is 1,0 the only correct answer choice?

Looking at the answer choices, only 1,0 creates a number ending in 0. The others (2,2), (1,3), and (4,2) all create numbers ending in 2, 3, or 2 respectively - none divisible by 10.

Divisibility Rules with Missing Digits

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

$51\text{ }_{—\text{ —}}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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

00:04 A number divisible by 10 is a number with 0 as its units digit

00:10 According to this method, we will go through all numbers and eliminate accordingly

00:21 And this is the solution to the question

Step-by-step written solution

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Understand the problem

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

$51\text{ }_{—\text{ —}}$

Step-by-step solution

To solve this problem, we'll focus on ensuring divisibility by 10 for the given number $51\text{ }_{—\text{ —}}$ .

The divisibility rule for 10 states that a number must end with the digit 0 to be divisible by 10.

Thus, the missing digits should form a number that ends in 0. Given the partial number $51\text{ }_{1\text{ —}}$ , we need to check potential combinations that satisfy this rule.

Evaluation of the required final digit: Only the digit 0 satisfies the condition for divisibility by 10, meaning the complete number should be $51y0$ where $y$ is any digit.

Hence, the missing sequence to ensure divisibility by 10 is $1, 0$ . Therefore, $51\text{ }_{1\text{ }0}$ is the solution.

Returning to the choices provided, the correct answer is choice 1: $1, 0$ .

To conclude, the number is completed as $5110$ , which is divisible by 10.

Final Answer

1, 0

Key Points to Remember

Essential concepts to master this topic

Rule: Numbers divisible by 10 must end with 0
Technique: For $51__$ , only patterns ending in 0 work
Check: Verify $5110 ÷ 10 = 511$ with no remainder ✓

Common Mistakes

Avoid these frequent errors

Choosing digits that don't end in 0
Don't pick combinations like 2,2 or 1,3 just because they look reasonable = numbers not divisible by 10! These create 5122 or 5113, which leave remainders when divided by 10. Always ensure the final digit is 0 for divisibility by 10.

Practice Quiz

Test your knowledge with interactive questions

Is the number 10 divisible by 4?

FAQ

Everything you need to know about this question

Why must the last digit be 0 for divisibility by 10?

Because 10 = 2 × 5, a number must be divisible by both 2 and 5. Only numbers ending in 0 satisfy both conditions - they're even (divisible by 2) and end in 0 or 5 (divisible by 5).

Can the first missing digit be any number?

Yes! Since we need $51_0$ , the third digit can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. All would make valid numbers divisible by 10.

How do I quickly check if a number is divisible by 10?

Simply look at the last digit! If it's 0, the entire number is divisible by 10. No calculation needed - it's that easy!

What if there were more missing digits?

The same rule applies! No matter how many digits are missing, the final digit must always be 0. The other missing digits can be any numbers from 0-9.

Why is 1,0 the only correct answer choice?

Looking at the answer choices, only 1,0 creates a number ending in 0. The others (2,2), (1,3), and (4,2) all create numbers ending in 2, 3, or 2 respectively - none divisible by 10.

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