203 LearnersLast updated on May 26th, 2025
Divisibility Rule of 789
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 789.
What is the Divisibility Rule of 789?
The divisibility rule for 789 is a method by which we can find out if a number is divisible by 789 or not without using the division method. Unfortunately, there is no simple standard rule like those for smaller numbers, as 789 is a composite number with multiple factors. However, you can check divisibility by verifying divisibility by each of its prime factors (3, 263) or calculate directly.
Example: Check whether 1575789 is divisible by 789 using prime factorization.
Step 1: Check divisibility by 3 (sum of digits method). The sum of the digits (1+5+7+5+7+8+9) is 42, which is divisible by 3.
Step 2: Check divisibility by 263 using long division or a calculator. Since 1575789 divided by 263 results in a whole number, it is divisible by 263.
Since 1575789 is divisible by both 3 and 263, it is divisible by 789.
Tips and Tricks for Divisibility Rule of 789
Familiarize with Prime Factors:
Knowing the prime factors of 789 (3, 263) will help in checking divisibility quickly.
Use Sum of Digits for 3:
A number is divisible by 3 if the sum of its digits is divisible by 3.
Long Division for Large Primes:
Use long division or a calculator for primes like 263 to verify divisibility.
Practice with Smaller Numbers:
Start with smaller numbers to understand the concept before applying it to larger numbers.
Use a Calculator for Verification:
A calculator can be used to verify results and ensure accuracy.
Common Mistakes and How to Avoid Them in Divisibility Rule of 789
The divisibility rule of 789 can be complex due to its prime factors. Here are some common mistakes and how to avoid them:
Mistake 1
Not checking all prime factors.
Ensure you check divisibility by all prime factors (3, 263).
Mistake 2
Incorrect sum of digits for divisibility by 3.
Double-check the sum of digits to ensure it is correct.
Mistake 3
Assuming divisibility by one factor implies divisibility by 789.
A number must be divisible by all prime factors of 789 to be divisible by 789.
Mistake 4
Forgetting to verify large numbers with a calculator.
Use a calculator for large numbers to confirm divisibility.
Mistake 5
Confusion between 789 and other similar numbers.
Focus on the specific factors of 789 to avoid confusion.
Divisibility Rule of 789 Examples
Problem 1
Is the number of pages in a book, 789, divisible by 789?
Yes, 789 is divisible by 789.
Explanation
Any number is divisible by itself, so 789 is divisible by 789. When you divide 789 by 789, the result is 1.
Problem 2
A shipment contains 1578 boxes. Can these be evenly distributed into groups of 789?
Yes, 1578 is divisible by 789.
Explanation
Divide 1578 by 789, and you get 2 as the quotient with no remainder. This means you can evenly distribute the boxes into 2 groups of 789 each.
Problem 3
An art installation requires 2367 light bulbs. Is it possible to arrange them in clusters of 789?
No, 2367 is not divisible by 789.
Explanation
Dividing 2367 by 789 gives a quotient of 3 with a remainder, indicating that the bulbs cannot be evenly arranged into clusters of 789
Problem 4
A marathon has 3156 participants. Can they be organized into teams of 789?
Yes, 3156 is divisible by 789.
Explanation
When you divide 3156 by 789, you get 4 as a quotient with no remainder. Therefore, the participants can be evenly divided into 4 teams of 789.
Problem 5
A factory produces 5000 widgets every day. Can the daily production be packed into boxes of 789 widgets each without any leftovers?
No, 5000 is not divisible by 789.
Explanation
Dividing 5000 by 789 results in a quotient with a remainder, indicating that the widgets cannot be packed evenly into boxes of 789 without leftovers.
FAQs on Divisibility Rule of 789
1. What is the divisibility rule for 789?
2.How can I check if a number is divisible by 3?
3.Is 789 a prime number?
4.Can I use a calculator to check divisibility by 789?
5.Does the divisibility rule of 789 apply to all integers?
6.How can children in Australia use numbers in everyday life to understand Divisibility Rule of 789?
7.What are some fun ways kids in Australia can practice Divisibility Rule of 789 with numbers?
8.What role do numbers and Divisibility Rule of 789 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 789 skills?
Important Glossaries for Divisibility Rule of 789
- Divisibility Rule: A set of guidelines used to determine if one number is divisible by another without performing full division.
- Prime Factor: A prime number that divides another number exactly without leaving a remainder.
- Composite Number: A number that has more than two factors, such as 789.
- Sum of Digits: The result obtained by adding all the digits of a number, used for checking divisibility by 3.
- Long Division: A method of dividing larger numbers to verify divisibility by less common factors.
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