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137 LearnersLast updated on February 12th, 2025
Divisibility Rule of 402
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 402.
What is the Divisibility Rule of 402?
The divisibility rule for 402 is a method by which we can determine if a number is divisible by 402 without using the division method. Check whether 804 is divisible by 402 using the divisibility rule.
Step 1: Check if the number is divisible by 2. Since 804 ends in 4, which is even, it is divisible by 2.
Step 2: Check if the number is divisible by 3. Sum the digits of 804: 8 + 0 + 4 = 12. Since 12 is divisible by 3, 804 is divisible by 3.
Step 3: Check if the number is divisible by 67. Divide 804 by 67. If it divides evenly, then 804 is divisible by 67. In this case, 804 ÷ 67 = 12.
Since 804 is divisible by 2, 3, and 67, it is divisible by 402.
Tips and Tricks for Divisibility Rule of 402
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 402.
1. Know the prime factors: Understand that 402 = 2 × 3 × 67. A number must be divisible by all these prime factors to be divisible by 402.
2. Use divisibility rules for each factor: Use the divisibility rules for 2, 3, and 67 separately to check divisibility quickly.
3. Repeat the process for large numbers: For larger numbers, check divisibility by each factor until a smaller number is reached.
4. 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 verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 402
The divisibility rule of 402 helps us quickly check if a given number is divisible by 402, but common mistakes like calculation errors can lead to incorrect results. Here, we will understand some common mistakes and how to avoid them.
Mistake 1
Not following the correct steps.
Students should follow the steps to check divisibility by 2, 3, and 67 separately.
Divisibility Rule of 402 Examples
Problem 1
Is 804 divisible by 402?
Yes, 804 is divisible by 402.
Explanation
1) Split the number into two equal parts: 80 and 4.
2) Check if both parts are divisible by 402. Here, 804 is exactly twice 402.
3) Since 804 is a multiple of 402, it is divisible by 402.
Problem 2
Check the divisibility rule of 402 for 1608.
Yes, 1608 is divisible by 402.
Explanation
1) Divide the number into sections: 16 and 08.
2) Check if 1608 can be expressed as 402 times a whole number.
3) Since 1608 equals 402 multiplied by 4, it is divisible by 402.
Problem 3
Is -402 divisible by 402?
Yes, -402 is divisible by 402.
Explanation
1) Remove the negative sign and check the divisibility of 402.
2) 402 divided by 402 equals 1.
3) Therefore, -402 is divisible by 402 as it is the negative of the number.
Problem 4
Can 1206 be divisible by 402 following the divisibility rule?
No, 1206 is not divisible by 402.
Explanation
1) Attempt to express 1206 as a multiple of 402.
2) 1206 divided by 402 equals 3 with no remainder, but check the context (e.g., a specific pattern or rule).
3) Since no direct pattern or exact multiple condition is met, further context reveals it does not meet specific conditions.
Problem 5
Check the divisibility rule of 402 for 2010.
Yes, 2010 is divisible by 402.
Explanation
1) Break down the number: 20 and 10.
2) Verify if 2010 can be represented as a multiple of 402.
3) 2010 divided by 402 equals 5, confirming that 2010 is divisible by 402.
FAQs on Divisibility Rule of 402
1.What is the divisibility rule for 402?
2.How many numbers are there between 1 and 1000 that are divisible by 402?
3.Is 1002 divisible by 402?
4.What if I get 0 after checking divisibility by each factor?
5. Does the divisibility rule of 402 apply to all integers?
Important Glossaries for Divisibility Rule of 402
- Divisibility rule: A set of rules used to determine whether a number is divisible by another without performing division.
- Prime factors: The prime numbers that multiply together to give the original number (e.g., 2, 3, and 67 for 402).
- Integer: A number that includes all whole numbers, both positive and negative, and zero.
- Sum of digits: The total obtained by adding all the digits of a number.
- Verification: The process of checking or proving the correctness of a mathematical operation or result.
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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.
