227 LearnersLast updated on May 26th, 2025
Divisibility Rule of 630
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 630.
What is the Divisibility Rule of 630?
The divisibility rule for 630 is a method by which we can find out if a number is divisible by 630 or not without using the division method. Check whether 12,600 is divisible by 630 with the divisibility rule.
Step 1: Ensure the number is divisible by 2, 3, 5, and 7, as 630 is the product of these primes.
- Check divisibility by 2: The last digit of 12,600 is 0, which is even.
- Check divisibility by 3: Sum the digits (1+2+6+0+0 = 9), and 9 is divisible by 3.
- Check divisibility by 5: The last digit is 0, which is divisible by 5.
- Check divisibility by 7: Use the rule for 7: double the last digit (0×2=0), subtract from the rest (1260-0=126), and see that 126 is divisible by 7 (as 126 divided by 7 equals 18 without a remainder).
Step 2: Since 12600 is divisible by 2, 3, 5, and 7, it is also divisible by 630.
Tips and Tricks for Divisibility Rule of 630
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 630.
1. Break Down the Rule:
- Remember that 630 = 2 × 3 × 5 × 7. So, check divisibility by each of these numbers.
2. Know the Prime Factors:
- Memorize the prime factors (2, 3, 5, and 7) to quickly apply the divisibility rules for each.
3. Use the Division Method to Verify:
- Students can use the division method as a way to verify and crosscheck their results. This will help them to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 630
The divisibility rule of 630 helps us quickly check if a given number is divisible by 630, but common mistakes like calculation errors can lead to incorrect conclusions. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not checking for all prime factors.
Ensure that you check divisibility by 2, 3, 5, and 7.
Mistake 2
Forgetting to apply all relevant divisibility rules.
Remember that a number must satisfy the divisibility rules for 2, 3, 5, and 7 to be divisible by 630.
Mistake 3
Miscalculating sums or products.
Double-check calculations, especially when summing digits or multiplying.
Mistake 4
Confusing the steps.
Practice regularly to remember the sequence of checks for each prime factor.
Divisibility Rule of 630 Examples
Problem 1
Is the number of pages in a book, 1890, divisible by 630?
Yes, 1890 is divisible by 630.
Explanation
To check if 1890 is divisible by 630, verify divisibility by 2, 3, 5, and 7 (since 630 = 2 × 3 × 5 × 7).
1) Divisibility by 2: The last digit is 0, which is even.
2) Divisibility by 3: Sum of digits is 1 + 8 + 9 + 0 = 18, and 18 is divisible by 3.
3) Divisibility by 5: The last digit is 0, which ends in 0 or 5.
4) Divisibility by 7: Apply the rule for 7: Double the last digit (0 × 2 = 0) and subtract from the rest (189 - 0 = 189). Check 189: 18 - (9 × 2) = 0, which is divisible by 7.
All conditions are met, so 1890 is divisible by 630.
Problem 2
A factory produces 3780 widgets in a batch. Is this number divisible by 630?
Yes, 3780 is divisible by 630.
Explanation
Check divisibility by 2, 3, 5, and 7:
1) Divisibility by 2: The last digit is 0, which is even.
2) Divisibility by 3: Sum of digits is 3 + 7 + 8 + 0 = 18, and 18 is divisible by 3.
3) Divisibility by 5: The last digit is 0, which ends in 0 or 5.
4) Divisibility by 7: Apply the rule: Double the last digit (0 × 2 = 0) and subtract from the rest (378 - 0 = 378). Check 378: 37 - (8 × 2) = 21, and 21 is divisible by 7.
All divisibility conditions are satisfied, thus 3780 is divisible by 630.
Problem 3
A conference room can hold 2520 chairs. Is this number divisible by 630?
No, 2520 is not divisible by 630.
Explanation
Check divisibility by 2, 3, 5, and 7:
1) Divisibility by 2: The last digit is 0, which is even.
2) Divisibility by 3: Sum of digits is 2 + 5 + 2 + 0 = 9, and 9 is divisible by 3.
3) Divisibility by 5: The last digit is 0, which ends in 0 or 5.
4) Divisibility by 7: Apply the rule: Double the last digit (0 × 2 = 0) and subtract from the rest (252 - 0 = 252). Check 252: 25 - (2 × 2) = 21, and 21 is divisible by 7.
Although 2520 satisfies divisibility by 2, 3, 5, and 7 individually, we must verify the least common multiple condition: 2520 is not divisible by the full product 630, as 2520 ÷ 630 = 4 with no remainder.
Problem 4
A shipment contains 5040 items. Can we evenly distribute them into groups of 630?
Yes, 5040 is divisible by 630.
Explanation
Check divisibility by 2, 3, 5, and 7:
1) Divisibility by 2: The last digit is 0, which is even.
2) Divisibility by 3: Sum of digits is 5 + 0 + 4 + 0 = 9, and 9 is divisible by 3.
3) Divisibility by 5: The last digit is 0, which ends in 0 or 5.
4) Divisibility by 7: Apply the rule: Double the last digit (0 × 2 = 0) and subtract from the rest (504 - 0 = 504). Check 504: 50 - (4 × 2) = 42, and 42 is divisible by 7.
All conditions are fulfilled, so 5040 is divisible by 630.
Problem 5
A charity event plans to distribute 3150 donated items equally among groups of 630. Is 3150 divisible by 630?
No, 3150 is not divisible by 630.
Explanation
Check divisibility by 2, 3, 5, and 7:
1) Divisibility by 2: The last digit is 0, which is even.
2) Divisibility by 3: Sum of digits is 3 + 1 + 5 + 0 = 9, and 9 is divisible by 3.
3) Divisibility by 5: The last digit is 0, which ends in 0 or 5.
4) Divisibility by 7: Apply the rule: Double the last digit (0 × 2 = 0) and subtract from the rest (315 - 0 = 315). Check 315: 31 - (5 × 2) = 21, and 21 is divisible by 7.
Although 3150 satisfies divisibility by 2, 3, 5, and 7, it is not divisible by 630 because 3150 ÷ 630 = 5 with a remainder.
FAQs on Divisibility Rule of 630
1.What is the divisibility rule for 630?
2.How many numbers between 1 and 10,000 are divisible by 630?
3.Is 3,150 divisible by 630?
4.What if I get 0 after checking divisibility by 7?
5.Does the divisibility rule of 630 apply to all integers?
6.How can children in Australia use numbers in everyday life to understand Divisibility Rule of 630?
7.What are some fun ways kids in Australia can practice Divisibility Rule of 630 with numbers?
8.What role do numbers and Divisibility Rule of 630 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Divisibility Rule of 630 skills?
Important Glossaries for Divisibility Rule of 630
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number without performing division.
- Prime factors: The prime numbers that multiply together to give the original number. For 630, these are 2, 3, 5, and 7.
- Multiples: Numbers that can be divided by a specific number without leaving a remainder. For example, multiples of 630 include 630, 1260, 1890, etc.
- Integer: A whole number that can be positive, negative, or zero.
- Subtraction: A mathematical operation that represents the operation of removing objects from a collection. Used in checking divisibility by 7.
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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.
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