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120 LearnersLast updated on February 26th, 2025
Divisibility Rule of 900
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 900.
What is the Divisibility Rule of 900?
The divisibility rule for 900 is a method by which we can find out if a number is divisible by 900 or not without using the division method. Check whether 5400 is divisible by 900 with the divisibility rule.
Step 1: Check if the number is divisible by both 100 and 9, since 900 = 100 × 9.
Step 2: To check divisibility by 100, the last two digits of the number should be 00. In 5400, the last two digits are 00, so it is divisible by 100.
Step 3: To check divisibility by 9, sum the digits of the number. For 5400, 5 + 4 + 0 + 0 = 9. Since 9 is divisible by 9, the number is divisible by 9.
Step 4: Since 5400 is divisible by both 100 and 9, it is divisible by 900.
Tips and Tricks for Divisibility Rule of 900
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 900.
Know the multiples of 900:
Memorize the multiples of 900 (900, 1800, 2700, 3600, etc.) to quickly check divisibility. If the result meets both criteria of divisibility by 100 and 9, then the number is divisible by 900.
Use the digit sum for the divisibility of 9:
If the sum of the digits is a multiple of 9, then the number is divisible by 9.
Repeat the process for large numbers:
Students should keep repeating the divisibility process until they reach a number that is manageable to work with using the divisibility rules for 100 and 9.
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 900
The divisibility rule of 900 helps us quickly check if a given number is divisible by 900, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes to help you avoid them.
Mistake 1
Not following the correct steps.
Students should follow the correct steps of checking divisibility by both 100 and 9.
Divisibility Rule of 900 Examples
Problem 1
Divisibility Rule of 900 Examples
Yes, 4500 widgets can be produced in batches of 900.
Explanation
To check if 4500 is divisible by 900, we divide 4500 by 900. The result is 4500 ÷ 900 = 5, which is a whole number. Therefore, 4500 is divisible by 900.
Problem 2
Is a shipment of 7200 kilograms of grain divisible into packages of 900 kilograms each?
Yes, 7200 kilograms can be divided into packages of 900 kilograms.
Explanation
To determine if 7200 is divisible by 900, divide 7200 by 900. The result is 7200 ÷ 900 = 8, which is an integer. Thus, 7200 is divisible by 900.
Problem 3
Can a budget of $8100 be divided evenly among 9 departments, with each receiving an amount divisible by 900?
Yes, $8100 can be divided evenly among 9 departments, with each receiving an amount divisible by 900.
Explanation
First, divide 8100 by 9 to find the amount each department receives: 8100 ÷ 9 = 900. Since 900 is divisible by 900, the budget can be evenly distributed.
Problem 4
Can 2700 units of a product be packaged in boxes that hold 900 units each?
Yes, 2700 units can be packaged in boxes that hold 900 units each.
Explanation
To check if 2700 is divisible by 900, divide 2700 by 900. The result is 2700 ÷ 900 = 3, which is a whole number. Thus, 2700 is divisible by 900.
Problem 5
Is it possible to divide a library of 3600 books into sections of 900 books each?
Yes, 3600 books can be divided into sections of 900 books each.
Explanation
To verify divisibility, divide 3600 by 900. The result is 3600 ÷ 900 = 4, which is an integer. Therefore, 3600 is divisible by 900.
FAQs on Divisibility Rule of 900
1.What is the divisibility rule for 900?
2.How many numbers are there between 1 and 10000 that are divisible by 900?
3.Is 2700 divisible by 900?
4.What if I get 0 after summing the digits for 9?
5.Does the divisibility rule of 900 apply to all integers?
Important Glossaries for Divisibility Rule of 900
- Divisibility Rule: The set of rules used to find out whether a number is divisible by another number or not. For example, a number is divisible by 900 if it is divisible by both 100 and 9.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 900 are 900, 1800, 2700, etc.
- Integers: Integers are the numbers that include all whole numbers, negative numbers, and zero.
- Sum of Digits: The addition of all digits in a number to check divisibility by 9.
- Last Two Digits: The last two digits of a number, used to check divisibility by 100.
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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.
