214 LearnersLast updated on May 26th, 2025
Divisibility Rule of 210
The divisibility rule is a way to find out whether a number is divisible by another number without using the division method. In real life, we can use the divisibility rule for quick math, dividing things evenly, and sorting things. In this topic, we will learn about the divisibility rule of 210.
What is the Divisibility Rule of 210?
The divisibility rule for 210 is a method by which we can find out if a number is divisible by 210 or not without using the division method. A number is divisible by 210 if it is divisible by 2, 3, 5, and 7.
Example: Check whether 2310 is divisible by 210 using the divisibility rule.
Step 1: Check divisibility by 2. A number is divisible by 2 if it ends in an even digit. 2310 ends in 0, which is even, so it is divisible by 2.
Step 2: Check divisibility by 3. A number is divisible by 3 if the sum of its digits is divisible by 3. 2 + 3 + 1 + 0 = 6, which is divisible by 3, so 2310 is divisible by 3.
Step 3: Check divisibility by 5. A number is divisible by 5 if it ends in 0 or 5. 2310 ends in 0, so it is divisible by 5.
Step 4: Check divisibility by 7. Use the divisibility rule for 7: Double the last digit and subtract it from the rest of the number. If the result is divisible by 7, the original number is as well. 2310: Double 0 to get 0, subtract from 231 to get 231. Double 1 to get 2, subtract from 23 to get 21, which is divisible by 7.
Since 2310 is divisible by all these numbers, it is divisible by 210.
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Tips and Tricks for Divisibility Rule of 210
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 210.
Know the multiples of 210:
Memorize the multiples of 210 (210, 420, 630, 840, 1050, etc.) to quickly check divisibility. If a number is a multiple of 210, it is divisible by 210.
Verify with smaller rules:
Check divisibility by 2, 3, 5, and 7 separately to ensure the number is divisible by 210.
Repeat the process for large numbers:
For large numbers, apply the divisibility rules repeatedly until you reach smaller numbers.
Example: Check if 44100 is divisible by 210 using the divisibility test.
- Divisible by 2: Ends in 0, so yes.
- Divisible by 3: Sum of digits 4 + 4 + 1 + 0 + 0 = 9, which is divisible by 3, so yes.
- Divisible by 5: Ends in 0, so yes.
- Divisible by 7: Double 0 to get 0, subtract from 441 to get 441. Double 1 to get 2, subtract from 44 to get 42, which is divisible by 7, so yes.
Since all conditions are met, 44100 is divisible by 210.
Use the division method to verify:
Use division to crosscheck results. This will help verify and also reinforce learning.
Common Mistakes and How to Avoid Them in Divisibility Rule of 210
The divisibility rule of 210 helps us quickly check if a number is divisible by 210, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not checking all divisibility rules.
Ensure to check divisibility by 2, 3, 5, and 7 to confirm divisibility by 210.
Mistake 2
Misapplying the rule for 7.
Double the last digit and subtract it correctly from the rest of the digits.
Mistake 3
Not repeating the process for large numbers.
Continue applying divisibility checks until the number is manageable.
Mistake 4
Ignoring zeros in calculations.
Do not overlook zeros; they affect divisibility by 5 and 2.
Mistake 5
Confusing the steps for different divisibility checks.
Practice regularly to remember the steps for each divisibility rule.
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Divisibility Rule of 210 Examples
Problem 1
A farmer has 630 apples and wants to pack them into boxes containing exactly 210 apples each. Can the farmer do this without any apples left over?
Yes, 630 is divisible by 210.
Explanation
To determine if 630 is divisible by 210, we need to check if it is divisible by all prime factors of 210 (2, 3, 5, and 7).
1. Check divisibility by 2: 630 is even, so it is divisible by 2.
2. Check divisibility by 3: Sum of digits \(6 + 3 + 0 = 9\), which is divisible by 3.
3. Check divisibility by 5: The last digit is 0, which is divisible by 5.
4. Check divisibility by 7 using the rule: \(63 - (0 \times 2) = 63\). Since 63 is divisible by 7, 630 is divisible by 7.
Since 630 is divisible by all these prime factors, it is divisible by 210.
Problem 2
A school is organizing a field trip and needs to arrange students into groups of 210. If there are 1050 students, can they be arranged into such groups without any students left out?
Yes, 1050 is divisible by 210.
Explanation
To check divisibility by 210, ensure divisibility by 2, 3, 5, and 7:
1. Check divisibility by 2: 1050 is even.
2. Check divisibility by 3: Sum of digits \(1 + 0 + 5 + 0 = 6\), which is divisible by 3.
3. Check divisibility by 5: The last digit is 0.
4. Check divisibility by 7 using the rule: \(105 - (0 \times 2) = 105\). Since 105 is divisible by 7, 1050 is too.
Thus, 1050 is divisible by 210.
Problem 3
A concert hall has 210 seats in a row. If there are 1680 people attending the concert, can they fill the rows completely without any seats left empty?
Yes, 1680 is divisible by 210.
Explanation
Verify divisibility by the factors of 210:
1. Check divisibility by 2: 1680 is even.
2. Check divisibility by 3: Sum of digits \(1 + 6 + 8 + 0 = 15\), which is divisible by 3.
3. Check divisibility by 5: The last digit is 0.
4. Check divisibility by 7 using the rule: \(168 - (0 \times 2) = 168\). Since 168 is divisible by 7, 1680 is divisible by 7.
Thus, 1680 is divisible by 210.
Problem 4
A company packages chocolates in boxes of 210. If they have 2520 chocolates, can all chocolates be packed without any leftover?
Yes, 2520 is divisible by 210.
Explanation
Check for divisibility by all prime factors:
1. Check divisibility by 2: 2520 is even.
2. Check divisibility by 3: Sum of digits \(2 + 5 + 2 + 0 = 9\), divisible by 3.
3. Check divisibility by 5: The last digit is 0.
4. Check divisibility by 7 using the rule: \(252 - (0 \times 2) = 252\). Since 252 is divisible by 7, 2520 is too.
Therefore, 2520 is divisible by 210.
Problem 5
A library is organizing its books in stacks of 210 for an exhibition. If they have 1890 books, can they organize them without any books left?
Yes, 1890 is divisible by 210.
Explanation
Confirm divisibility by 2, 3, 5, and 7:
1. Check divisibility by 2: 1890 is even.
2. Check divisibility by 3: Sum of digits \(1 + 8 + 9 + 0 = 18\), divisible by 3.
3. Check divisibility by 5: The last digit is 0.
4. Check divisibility by 7 using the rule: \(189 - (0 \times 2) = 189\). Since 189 is divisible by 7, 1890 is divisible by 7.
Thus, 1890 is divisible by 210.
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FAQs on Divisibility Rule of 210
1. What is the divisibility rule for 210?
2.How many numbers are there between 1 and 1000 that are divisible by 210?
3.Is 420 divisible by 210?
4.What if I get 0 during calculations?
5. Does the divisibility rule of 210 apply to all the integers?
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Important Glossaries for Divisibility Rule of 210
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
- Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 210 are 210, 420, 630, etc.
- Integers: Numbers that include all whole numbers, negative numbers, and zero.
- Subtraction: A process of finding the difference between two numbers by reducing one number from another.
- Even number: A number divisible by 2, such as 0, 2, 4, 6, 8, etc.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
