$ 8534 $ with a remainder of 2

$ 6321 $ with a remainder of 3

$ 8124 $ with a remainder of 0

Divisibility Test: Is 652023 Divisible by 6?

Q: Why do I start with 52 instead of just 5?

Because 6 doesn't go into 5! You need the smallest group of digits where the divisor fits. Since 6 > 5, you take the first two digits: 52.

Q: What if I get confused about where to put each digit in the quotient?

Each digit in the quotient goes directly above the last digit you brought down. For 52023÷6, the first 8 goes above the 2 in 52.

Q: How do I know when to stop dividing?

Stop when the remaining number is smaller than your divisor. In this case, we end with 3, which is less than 6, so 3 becomes our remainder.

Q: Is there a faster way to check if 52023 is divisible by 6?

Yes! A number is divisible by 6 if it's divisible by both 2 and 3. Since 52023 ends in 3 (odd), it's not divisible by 2, so it can't be divisible by 6.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's solve this problem, step by step.

00:13 First, check the leftmost digit of the dividend.

00:18 Since 5 is less than 6, let's add the next digit and divide.

00:24 Write the quotient above, keeping the position precise.

00:30 Next, multiply the quotient by the divisor.

00:34 Subtract the product from the current number.

00:37 Bring down the next digit to continue.

00:41 Now, divide again with the new number.

00:44 Carefully place the result in the right position.

00:49 Multiply, and then subtract to see what's left.

00:53 Again, bring down the next digit.

00:57 Let's divide once more with our new number.

01:01 Position the result carefully above.

01:04 Multiply and subtract again to continue.

01:09 Bring down the next digit and repeat.

01:16 Divide with the latest number.

01:19 Write the quotient properly, keeping it neat.

01:23 Multiply, and then subtract one more time.

01:27 We end up with a remainder of 3.

01:31 And that's how we solved the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

2

Step-by-step solution

To solve the problem of dividing 52023 by 6, follow these steps:

Step 1: Set up the division of 52023 by 6.
Step 2: Begin by seeing how many times 6 goes into the first digit(s). Since 6 does not go into 5, consider the first two digits, 52.
Step 3: Divide 52 by 6, which gives 8. Since 6 times 8 is 48, place 8 in the tens place, multiply, and subtract: 52 - 48 = 4.
Step 4: Bring down the next digit (0), making 40.
Step 5: Divide 40 by 6, which gives 6 since 6 times 6 is 36. Write 6 next to 8 in the quotient, multiply and subtract: 40 - 36 = 4.
Step 6: Bring down the next digit (2), making 42.
Step 7: Divide 42 by 6, which gives 7. Write 7 next to 66 in the quotient: 42 - 42 = 0.
Step 8: Bring down the final digit (3), making 3.
Step 9: 6 doesn't go into 3, so write a 0 in the quotient and the remainder is 3.

Performing the above steps, we find that dividing 52023 by 6 gives a quotient of $8670$ and a remainder of 3.

The final solution includes both the quotient and remainder:

$8670$ with a remainder of 3.

3

Final Answer

$8670$ with a remainder of 3

Key Points to Remember

Essential concepts to master this topic

Setup: Start with largest digit grouping where divisor fits
Technique: For 52÷6: 8×6=48, subtract to get remainder 4
Check: Quotient×divisor + remainder = original: 8670×6+3=52023 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to bring down digits properly
Don't skip bringing down the next digit after each division step = incomplete quotient! This leaves you with wrong partial results. Always bring down one digit at a time and complete each division before moving to the next.

Practice Quiz

Test your knowledge with interactive questions

FAQ

Everything you need to know about this question

Why do I start with 52 instead of just 5?

+

Because 6 doesn't go into 5! You need the smallest group of digits where the divisor fits. Since 6 > 5, you take the first two digits: 52.

What if I get confused about where to put each digit in the quotient?

+

Each digit in the quotient goes directly above the last digit you brought down. For 52023÷6, the first 8 goes above the 2 in 52.

How do I know when to stop dividing?

+

Stop when the remaining number is smaller than your divisor. In this case, we end with 3, which is less than 6, so 3 becomes our remainder.

Is there a faster way to check if 52023 is divisible by 6?

+

Yes! A number is divisible by 6 if it's divisible by both 2 and 3. Since 52023 ends in 3 (odd), it's not divisible by 2, so it can't be divisible by 6.

What does the remainder of 3 actually mean?

+

The remainder of 3 means that after dividing 52023 into groups of 6, you have 3 left over. So $52023 = 6 \times 8670 + 3$ .

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Divisibility Test: Is 652023 Divisible by 6?

Long Division with Remainder Calculation

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