184 LearnersLast updated on May 26th, 2025
Divisibility Rule of 75
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 75.
What is the Divisibility Rule of 75?
The divisibility rule for 75 is a method by which we can find out if a number is divisible by 75 or not without using the division method. Check whether 450 is divisible by 75 with the divisibility rule.
Step 1: Check if the number is divisible by 3. Add the digits of 450: 4 + 5 + 0 = 9. Since 9 is divisible by 3, proceed to the next step.
Step 2: Check if the number is divisible by 25. A number is divisible by 25 if its last two digits form a number that is divisible by 25. The last two digits of 450 are 50, which is divisible by 25.
Step 3: Since 450 passes both tests, it is divisible by 75.
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Tips and Tricks for Divisibility Rule of 75
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 75.
Know the multiples of 75:
Memorize the multiples of 75 (75, 150, 225, 300, 375, etc.) to quickly check divisibility. If the number matches one of these multiples, it is divisible by 75.
Use the divisibility rules for 3 and 25:
Ensure a number is divisible by both 3 and 25, as 75 is the product of these two numbers.
Repeat the process for large numbers:
For large numbers, break them down into smaller parts and apply the divisibility rules for 3 and 25 separately.
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 verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 75
The divisibility rule of 75 helps us to quickly check if the given number is divisible by 75, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes that will help you understand.
Mistake 1
Not following the correct steps.
Students should follow the correct steps that involve checking divisibility by both 3 and 25
Mistake 2
Ignoring one of the factors of 75.
Remember to verify divisibility by both 3 and 25.
Mistake 3
Miscalculating when adding digits for divisibility by 3.
Carefully add the digits and verify if the sum is divisible by 3.
Mistake 4
Not checking the last two digits for divisibility by 25.
Always ensure the last two digits form a number divisible by 25.
Mistake 5
Confusing the steps.
Students often confuse the steps or forget them; practice regularly to avoid this error.
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Divisibility Rule of 75 Examples
Problem 1
Is 225 divisible by 75?
Yes, 225 is divisible by 75.
Explanation
To check if 225 is divisible by 75, we follow these steps:
1) Check if the number is divisible by 3 (sum of digits is 2 + 2 + 5 = 9, which is divisible by 3).
2) Check if the number is divisible by 25 (the last two digits are 25, which is divisible by 25).
Since 225 meets both conditions, it is divisible by 75.
Problem 2
Can 450 be divided evenly by 75?
Yes, 450 is divisible by 75.
Explanation
To determine if 450 is divisible by 75, follow these checks:
1) Check divisibility by 3 (sum of digits is 4 + 5 + 0 = 9, which is divisible by 3).
2) Check divisibility by 25 (the last two digits are 50, which is divisible by 25).
Since 450 satisfies both conditions, it is divisible by 75.
Problem 3
Is 160 divisible by 75?
No, 160 is not divisible by 75.
Explanation
To check the divisibility of 160 by 75, perform the following checks:
1) Check divisibility by 3 (sum of digits is 1 + 6 + 0 = 7, which is not divisible by 3).
2) Check divisibility by 25 (the last two digits are 60, which is not divisible by 25).
Since 160 fails both checks, it is not divisible by 75.
Problem 4
Determine if 825 is divisible by 75.
Yes, 825 is divisible by 75.
Explanation
For checking divisibility of 825 by 75, follow these steps:
1) Check divisibility by 3 (sum of digits is 8 + 2 + 5 = 15, which is divisible by 3).
2) Check divisibility by 25 (the last two digits are 25, which is divisible by 25).
Since 825 meets both conditions, it is divisible by 75.
Problem 5
Is 980 divisible by 75?
No, 980 is not divisible by 75.
Explanation
To assess if 980 is divisible by 75, apply these checks:
1) Check divisibility by 3 (sum of digits is 9 + 8 + 0 = 17, which is not divisible by 3).
2) Check divisibility by 25 (the last two digits are 80, which is not divisible by 25).
Since 980 does not satisfy both conditions, it is not divisible by 75.
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FAQs on Divisibility Rule of 75
1.What is the divisibility rule for 75?
2.How many numbers are there between 1 and 500 that are divisible by 75?
3.Is 225 divisible by 75?
4.What if I get 0 after checking divisibility by 25?
5.Does the divisibility rule of 75 apply to all integers?
6.How can children in Philippines use numbers in everyday life to understand Divisibility Rule of 75?
7.What are some fun ways kids in Philippines can practice Divisibility Rule of 75 with numbers?
8.What role do numbers and Divisibility Rule of 75 play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve Divisibility Rule of 75 skills?
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Important Glossaries for Divisibility Rule of 75
- 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 3 if the sum of its digits is divisible by 3.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 75 are 75, 150, 225, 300, etc.
- Integers: Integers are numbers that include all whole numbers, negative numbers, and zero.
- Addition: Addition is the process of finding the total or sum by combining two or more numbers.
- Division: Division is a mathematical operation where a number is divided into equal parts.
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About BrightChamps in Philippines
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.
