229 LearnersLast updated on May 26th, 2025
Divisibility Rule of 408
The divisibility rule is a way to determine whether a number is divisible by another number without performing the division operation. In real life, we can use the divisibility rule for quick math, dividing things evenly, and sorting items. In this topic, we will learn about the divisibility rule of 408.
What is the Divisibility Rule of 408?
The divisibility rule for 408 helps us determine if a number is divisible by 408 without performing division. Check whether 1224 is divisible by 408 using the divisibility rule.
Step 1: Check if the number is divisible by 8. The last three digits of 1224 are 224, and 224 ÷ 8 = 28, so 224 is divisible by 8.
Step 2: Check if the number is divisible by 51 (since 408 = 8 × 51). The sum of the digits of 1224 is 1 + 2 + 2 + 4 = 9, and since 9 is not divisible by 3, 1224 is not divisible by 51.
Step 3: Since 1224 is not divisible by both 8 and 51, it is not divisible by 408.
Tips and Tricks for Divisibility Rule of 408
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 408.
Know the multiples of 408:
Familiarize yourself with the multiples of 408 (408, 816, 1224, 1632, etc.) to quickly check divisibility. If a number is a multiple of 408, then it is divisible by 408.
Use the sum of the digits for divisibility by 3:
If the sum of the digits of a number is divisible by 3, then the number is divisible by 3. This helps in checking divisibility by 51.
Repeat the process for large numbers:
For larger numbers, keep applying the divisibility tests for 8 and 51 until you can clearly determine divisibility by 408.
Use the division method to verify:
Students can use the division method to verify and cross-check their results, providing an additional layer of assurance.
Common Mistakes and How to Avoid Them in Divisibility Rule of 408
The divisibility rule of 408 helps us quickly check if a given number is divisible by 408, but common mistakes like calculation errors can lead to incorrect results. Here we will address some common mistakes and ways to avoid them.
Mistake 1
Not checking divisibility by both 8 and 51.
Ensure you check divisibility by 8 and 51, as 408 is the product of these numbers.
Mistake 2
Ignoring the sum of digits for divisibility by 3.
Always calculate the sum of the digits to check divisibility by 3, which is part of checking divisibility by 51.
Mistake 3
Not repeating the process for large numbers.
Continue applying the divisibility tests for 8 and 51 for larger numbers until you reach a clear conclusion.
Mistake 4
Confusing the divisibility rules for 8 and 51.
Practice regularly to avoid confusing these rules and ensure correct application.
Mistake 5
Using incorrect calculations.
Double-check your calculations to ensure accuracy.
Divisibility Rule of 408 Examples
Problem 1
Is 2448 divisible by 408?
Yes, 2448 is divisible by 408.
Explanation
To check if 2448 is divisible by 408, we can use the divisibility rule for 408, which is 408 = 2 × 2 × 2 × 3 × 17.
1) Check if the number is divisible by 8 (2 × 2 × 2): The last three digits are 448, and 448 ÷ 8 = 56, which is an integer, so it is divisible by 8.
2) Check if the number is divisible by 3: Sum the digits, 2 + 4 + 4 + 8 = 18, and 18 is divisible by 3.
3) Check if the number is divisible by 17: 2448 ÷ 17 = 144, which is an integer, so it is divisible by 17.
Since 2448 is divisible by 8, 3, and 17, it is divisible by 408.
Problem 2
Check the divisibility rule of 408 for 3672.
Yes, 3672 is divisible by 408.
Explanation
To check if 3672 is divisible by 408, which is 2 × 2 × 2 × 3 × 17, follow these steps:
1) Check divisibility by 8: The last three digits are 672, and 672 ÷ 8 = 84, which is an integer.
2) Check divisibility by 3: Sum the digits, 3 + 6 + 7 + 2 = 18, and 18 is divisible by 3.
3) Check divisibility by 17: 3672 ÷ 17 = 216, which is an integer.
Since 3672 is divisible by 8, 3, and 17, it is divisible by 408.
Problem 3
Is 816 not divisible by 408?
No, 816 is divisible by 408.
Explanation
To determine if 816 is divisible by 408, follow the rule for 408:
1) Check divisibility by 8: The last three digits are 816, and 816 ÷ 8 = 102, which is an integer.
2) Check divisibility by 3: Sum the digits, 8 + 1 + 6 = 15, and 15 is divisible by 3.
3) Check divisibility by 17: 816 ÷ 17 = 48, which is an integer.
Since 816 is divisible by 8, 3, and 17, it is divisible by 408.
Problem 4
Can 1236 be divisible by 408 following the divisibility rule?
No, 1236 is not divisible by 408.
Explanation
: To check if 1236 is divisible by 408, follow the steps for 408:
1) Check divisibility by 8: The last three digits are 236, and 236 ÷ 8 = 29.5, which is not an integer.
Therefore, 1236 is not divisible by 8, and thus, it is not divisible by 408.
Problem 5
Check the divisibility rule of 408 for 4896
Yes, 4896 is divisible by 408.
Explanation
To check if 4896 is divisible by 408, follow these steps:
1) Check divisibility by 8: The last three digits are 896, and 896 ÷ 8 = 112, which is an integer.
2) Check divisibility by 3: Sum the digits, 4 + 8 + 9 + 6 = 27, and 27 is divisible by 3.
3) Check divisibility by 17: 4896 ÷ 17 = 288, which is an integer.
Since 4896 is divisible by 8, 3, and 17, it is divisible by 408.
FAQs on Divisibility Rule of 408
1.What is the divisibility rule for 408?
2. How many numbers are there between 1 and 2000 that are divisible by 408?
3.Is 816 divisible by 408?
4.What if I get 0 after applying the divisibility tests?
5.Does the divisibility rule of 408 apply to all integers?
6.How can children in Thailand use numbers in everyday life to understand Divisibility Rule of 408?
7.What are some fun ways kids in Thailand can practice Divisibility Rule of 408 with numbers?
8.What role do numbers and Divisibility Rule of 408 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Divisibility Rule of 408 skills?
Important Glossaries for Divisibility Rule of 408
- Divisibility rule: A set of rules used to find out whether a number is divisible by another number without performing division.
- Multiples: The results obtained by multiplying a number by an integer. For example, multiples of 408 are 408, 816, 1224, 1632, etc.
- Integers: Numbers that include all whole numbers, negative numbers, and zero.
- Sum of digits: The total obtained by adding all digits of a number, used for checking divisibility by 3.
- Subtraction: The process of finding the difference between two numbers, not directly used here but important in other divisibility rules.
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About BrightChamps in Thailand
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.
