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118 LearnersLast updated on February 18th, 2025
Divisibility Rule of 870
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 870.
What is the Divisibility Rule of 870?
The divisibility rule for 870 is a method by which we can find out if a number is divisible by 870 or not without using the division method. Check whether 2610 is divisible by 870 with the divisibility rule.
Step 1: Check if the number is divisible by 10. The number 2610 ends in 0, so it is divisible by 10.
Step 2: Check if the number is divisible by 87. We need to check the divisibility by both 3 and 29 (since 87 = 3 × 29).
- For 3: Add the digits of the number and see if the sum is divisible by 3. 2+6+1+0 = 9, which is divisible by 3.
- For 29: Use the divisibility rule for 29 (usually involves specific calculations or direct division, but for simplicity, assume familiarity with divisibility by 29).
Step 3: Since 261 is divisible by 3 but not by 29, 2610 is not divisible by 870.
Tips and Tricks for Divisibility Rule of 870
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 870.
Know the multiples of 29:
Memorize the multiples of 29 (29, 58, 87, 116, 145, etc.) to quickly check divisibility. If the number is divisible by both 87 and 10, then it is divisible by 870.
Use direct division for large numbers: If the number is large, use direct division to check divisibility by 870.
Verify using smaller factors: Since 870 = 2 × 3 × 5 × 29, verify divisibility through these smaller factors.
Use the division method to verify:
Students can use the division method as a way to verify and cross-check their results. This will help them to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 870
The divisibility rule of 870 helps us quickly check if the given number is divisible by 870, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes that will help you to understand.
Mistake 1
Not considering all factors of 870.
Students should check divisibility by 10 and 87 (further broken into 3 and 29).
Divisibility Rule of 870 Examples
Problem 1
Is 2610 divisible by 870?
Yes, 2610 is divisible by 870.
Explanation
To determine if 2610 is divisible by 870, we can divide 2610 by 870.
1) Divide the number 2610 by 870.
2) 2610 ÷ 870 = 3.
3) Since the result is a whole number, 2610 is divisible by 870.
Problem 2
Check the divisibility rule of 870 for 3480.
No, 3480 is not divisible by 870.
Explanation
To check the divisibility of 3480 by 870:
1) Divide the number 3480 by 870.
2) 3480 ÷ 870 = 4 (with a remainder).
3) Since there is a remainder, 3480 is not divisible by 870.
Problem 3
Is -1740 divisible by 870?
Yes, -1740 is divisible by 870.
Explanation
To check if -1740 is divisible by 870:
1) Consider the absolute value and divide 1740 by 870.
2) 1740 ÷ 870 = 2.
3) The result is a whole number, so -1740 is divisible by 870.
Problem 4
Can 435 be divisible by 870 following the divisibility rule?
No, 435 is not divisible by 870.
Explanation
To check if 435 is divisible by 870:
1) Divide the number 435 by 870.
2) 435 ÷ 870 = 0 (with a remainder).
3) Since the quotient is not a whole number, 435 is not divisible by 870.
Problem 5
Check the divisibility rule of 870 for 5220.
Yes, 5220 is divisible by 870.
Explanation
To verify if 5220 is divisible by 870:
1) Divide 5220 by 870.
2) 5220 ÷ 870 = 6.
3) The result is a whole number, indicating that 5220 is divisible by 870.
FAQs on Divisibility Rule of 870
1.What is the divisibility rule for 870?
2.How many numbers are there between 1 and 1000 that are divisible by 870?
3.Is 2610 divisible by 870?
4.What if I get 0 after dividing?
5.Does the divisibility rule of 870 apply to all integers?
Important Glossaries for Divisibility Rule of 870
- Divisibility rule: A set of rules used to find out whether a number is divisible by another number without direct division.
- Multiples: Results obtained by multiplying a number by an integer, such as multiples of 29.
- Factors: Numbers that divide another number exactly without leaving a remainder.
- Division: The process of determining how many times one number is contained within another.
- Remainder: The amount left after division when one number does not divide the other exactly.
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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.
