113 LearnersLast updated on May 26th, 2025
Divisibility Rule of 78
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 78.
What is the Divisibility Rule of 78?
The divisibility rule for 78 is a method by which we can find out if a number is divisible by 78 or not without using the division method. A number is divisible by 78 if it is divisible by both 2 and 39. Let's check whether 624 is divisible by 78 using the divisibility rule.
Step 1: Check divisibility by 2. The last digit of 624 is 4, which is even, so 624 is divisible by 2.
Step 2: Check divisibility by 39. Divide the number into parts that are easy to handle: 624 can be broken into 600 and 24.
Check if 600 is divisible by 39. 600 ÷ 39 = 15.38, not an integer.
Check if 24 is divisible by 39. 24 ÷ 39 = 0.615, not an integer.
Since 624 is divisible by 2 but not by 39, it is not divisible by 78.
Tips and Tricks for Divisibility Rule of 78
Learning divisibility rules will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 78.
- Know the multiples of 78: Memorize the multiples of 78 (78, 156, 234, 312, etc.) to quickly check divisibility. If a number is one of these multiples, it is divisible by 78.
- Use the divisibility rules of 2 and 39: Break down the divisibility check into simpler parts by using the rules for 2 and 39.
- 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 to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 78
The divisibility rule of 78 helps us to quickly check if the given number is divisible by 78, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not checking divisibility by both 2 and 39.
Ensure you check divisibility by both 2 and 39, as both must be true for divisibility by 78.
Divisibility Rule of 78 Examples
Problem 1
Can 624 be divided evenly by 78?
Yes, 624 is divisible by 78.
Explanation
To determine if 624 is divisible by 78, we can use a simplified approach as 78 is made up of 2, 3, and 13 (since 78 = 2 x 3 x 13).
1) Check if 624 is divisible by 2: The last digit is 4, which is even, so it's divisible by 2.
2) Check if 624 is divisible by 3: Sum the digits, 6 + 2 + 4 = 12, which is divisible by 3.
3) Check if 624 is divisible by 13: Divide 624 by 13 and check if the result is a whole number. 624 ÷ 13 = 48, which is a whole number.
Since 624 is divisible by 2, 3, and 13, it is divisible by 78.
Problem 2
Determine if 780 is divisible by 78.
Yes, 780 is divisible by 78.
Explanation
To check if 780 is divisible by 78, we can verify the divisibility by its factors.
1) Check if 780 is divisible by 2: The last digit is 0, which is even, so it's divisible by 2.
2) Check if 780 is divisible by 3: Sum the digits, 7 + 8 + 0 = 15, which is divisible by 3.
3) Check if 780 is divisible by 13: Divide 780 by 13 and check if the result is a whole number. 780 ÷ 13 = 60, which is a whole number.
Since 780 is divisible by 2, 3, and 13, it is divisible by 78.
Problem 3
Is 234 not divisible by 78?
No, 234 is not divisible by 78.
Explanation
To determine if 234 is divisible by 78, check its divisibility by 2, 3, and 13.
1) Check if 234 is divisible by 2: The last digit is 4, which is even, so it's divisible by 2.
2) Check if 234 is divisible by 3: Sum the digits, 2 + 3 + 4 = 9, which is divisible by 3.
3) Check if 234 is divisible by 13: Divide 234 by 13 and check if the result is a whole number. 234 ÷ 13 = 18 with a remainder, which means it's not a whole number.
Since 234 is not divisible by 13, it is not divisible by 78.
Problem 4
Verify if 1014 is divisible by 78.
Yes, 1014 is divisible by 78.
Explanation
To check the divisibility of 1014 by 78, verify divisibility by 2, 3, and 13.
1) Check if 1014 is divisible by 2: The last digit is 4, which is even, so it's divisible by 2.
2) Check if 1014 is divisible by 3: Sum the digits, 1 + 0 + 1 + 4 = 6, which is divisible by 3.
3) Check if 1014 is divisible by 13: Divide 1014 by 13 and check if the result is a whole number. 1014 ÷ 13 = 78, which is a whole number.
Since 1014 is divisible by 2, 3, and 13, it is divisible by 78.
Problem 5
Is 5200 divisible by 78?
No, 5200 is not divisible by 78.
Explanation
To determine if 5200 is divisible by 78, check divisibility by 2, 3, and 13.
1) Check if 5200 is divisible by 2: The last digit is 0, which is even, so it's divisible by 2.
2) Check if 5200 is divisible by 3: Sum the digits, 5 + 2 + 0 + 0 = 7, which is not divisible by 3.
Since 5200 is not divisible by 3, it is not divisible by 78.
FAQs on Divisibility Rule of 78
1.What is the divisibility rule for 78?
2.How many numbers between 1 and 1000 are divisible by 78?
3.Is 312 divisible by 78?
4. What if I get 0 after checking divisibility conditions?
5.Does the divisibility rule of 78 apply to all integers?
6.How can children in Thailand use numbers in everyday life to understand Divisibility Rule of 78?
7.What are some fun ways kids in Thailand can practice Divisibility Rule of 78 with numbers?
8.What role do numbers and Divisibility Rule of 78 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 78 skills?
Important Glossary for Divisibility Rule of 78
- Divisibility Rule: The set of rules used to find out whether a number is divisible by another number or not.
- Multiples: Results we get after multiplying a number by an integer. For example, multiples of 78 are 78, 156, 234, etc.
- Integer: Numbers that include all whole numbers and their negatives, including zero.
- Even Number: A number divisible by 2, such as 2, 4, 6, etc.
- Verification: The process of checking or proving the accuracy of a calculation 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
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