156 LearnersLast updated on May 26th, 2025
Divisibility Rule of 156
The divisibility rule is a way to determine whether a number is divisible by another number without using the traditional division method. In real life, divisibility rules are useful for quick calculations, dividing things evenly, and sorting items. In this topic, we will learn about the divisibility rule of 156.
What is the Divisibility Rule of 156?
The divisibility rule for 156 is a method to find out if a number is divisible by 156 without using the division method. Let's check whether 18720 is divisible by 156 using the divisibility rule.
Step 1: Check if the number is divisible by 3, 4, and 13, as 156 is the product of these numbers (3 × 4 × 13 = 156).
Step 2: For divisibility by 3, sum all the digits. If the sum is a multiple of 3, the number is divisible by 3. In 18720, the sum is 1 + 8 + 7 + 2 + 0 = 18, which is divisible by 3.
Step 3: For divisibility by 4, check the last two digits. If they form a number divisible by 4, then the entire number is divisible by 4. Here, 20 is divisible by 4.
Step 4: For divisibility by 13, use the rule where you take the last digit, multiply it by 9, and subtract from the rest of the number. If the result is divisible by 13, then the number is divisible by 13. Here, multiply 0 by 9 and subtract from 1872, giving 1872, which is divisible by 13.
Since 18720 is divisible by 3, 4, and 13, it is also divisible by 156.
Tips and Tricks for Divisibility Rule of 156
Learn the divisibility rule to help master division. Let's explore a few tips and tricks for the divisibility rule of 156.
- Know the factors: Understand that 156 is the product of 3, 4, and 13. Check divisibility by these factors.
- Sum of digits for 3: Remember, if the sum of a number's digits is a multiple of 3, the number is divisible by 3.
- Last two digits for 4: Only the last two digits matter for divisibility by 4.
- Special rule for 13: Multiply the last digit by 9 and subtract from the remaining number to check for divisibility by 13.
- Verify with division: Use the division method to confirm and cross-check results.
Common Mistakes and How to Avoid Them in Divisibility Rule of 156
The divisibility rule of 156 helps us quickly check if a number is divisible by 156, but common mistakes like calculation errors can lead to incorrect results. Here, we will address some common mistakes and their solutions.
Mistake 1
Not checking all factors.
Ensure you check divisibility by 3, 4, and 13.
Divisibility Rule of 156 Examples
Problem 1
Is 1872 divisible by 156?
Yes, 1872 is divisible by 156.
Explanation
To check if 1872 is divisible by 156, we need to follow these steps:
1) Check if the number is divisible by 3. The sum of the digits (1 + 8 + 7 + 2 = 18) is divisible by 3.
2) Check if the number is divisible by 4. The last two digits, 72, are divisible by 4.
3) Check if the number is divisible by 13. Subtract 9 times the last digit from the rest of the number: 187 - (9 x 2) = 169, which is divisible by 13.
Since 1872 meets all these conditions, it is divisible by 156.
Problem 2
Check if 2496 is divisible by 156.
Yes, 2496 is divisible by 156.
Explanation
To verify the divisibility of 2496 by 156:
1) Check divisibility by 3: The sum of digits (2 + 4 + 9 + 6 = 21) is divisible by 3.
2) Check divisibility by 4: The last two digits, 96, are divisible by 4.
3) Check divisibility by 13: Subtract 9 times the last digit from the rest: 249 - (9 x 6) = 195, which is divisible by 13.
Since all conditions are satisfied, 2496 is divisible by 156.
Problem 3
Is 312 divisible by 156?
Yes, 312 is divisible by 156.
Explanation
To determine if 312 is divisible by 156:
1) Check divisibility by 3: The sum of digits (3 + 1 + 2 = 6) is divisible by 3.
2) Check divisibility by 4: The last two digits, 12, are divisible by 4.
3) Check divisibility by 13: Subtract 9 times the last digit from the rest of the number: 31 - (9 x 2) = 13, which is divisible by 13.
Hence, 312 is divisible by 156.
Problem 4
Can 429 be divisible by 156?
No, 429 is not divisible by 156.
Explanation
To check if 429 is divisible by 156:
1) Check divisibility by 3: The sum of digits (4 + 2 + 9 = 15) is divisible by 3.
2) Check divisibility by 4: The last two digits, 29, are not divisible by 4.
3) Even if we checked for divisibility by 13, the failure of divisibility by 4 is enough to conclude that 429 is not divisible by 156.
Problem 5
Is 624 divisible by 156?
Yes, 624 is divisible by 156.
Explanation
To verify the divisibility of 624 by 156:
1) Check divisibility by 3: The sum of digits (6 + 2 + 4 = 12) is divisible by 3.
2) Check divisibility by 4: The last two digits, 24, are divisible by 4.
3) Check divisibility by 13: Subtract 9 times the last digit from the rest: 62 - (9 x 4) = 26, which is divisible by 13.
Thus, 624 is divisible by 156.
FAQs on Divisibility Rule of 156
1. What is the divisibility rule for 156?
2.How many numbers between 1 and 1000 are divisible by 156?
3. Is 624 divisible by 156?
4.What if I get 0 after subtraction in the step for 13?
5. Does the divisibility rule of 156 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 156?
7.What are some fun ways kids in United States can practice Divisibility Rule of 156 with numbers?
8.What role do numbers and Divisibility Rule of 156 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Divisibility Rule of 156 skills?
Important Glossaries for Divisibility Rule of 156
- Divisibility rule: A set of guidelines used to determine if one number is divisible by another without performing division.
- Factors: Numbers that multiply together to form another number. For 156, the factors are 3, 4, and 13.
- Multiples: The result of multiplying a number by an integer. For example, multiples of 156 include 156, 312, etc.
- Sum of digits: The total obtained by adding all the digits of a number, used to check divisibility by 3.
- Subtraction: The process of taking one number away from another, used in the rule for divisibility by 13.
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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.
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