150 LearnersLast updated on May 26th, 2025
Divisibility Rule of 780
The divisibility rule is a way to determine whether a number is divisible by another number without performing actual division. In real life, we use divisibility rules for quick calculations, dividing items evenly, and organizing things. In this topic, we will learn about the divisibility rule of 780.
What is the Divisibility Rule of 780?
The divisibility rule for 780 helps us find out if a number is divisible by 780 without using the division method. Let's check whether 1560 is divisible by 780 using this rule.
Step 1: Check divisibility by 10. The last digit of 1560 is 0, so it is divisible by 10.
Step 2: Check divisibility by 78. To do this, check divisibility by both 6 and 13, since 78 = 6 × 13.
Step 3: For divisibility by 6, check divisibility by both 2 and 3:
- 1560 is divisible by 2 because the last digit is 0 (an even number).
- Sum the digits of 1560 (1 + 5 + 6 + 0 = 12), which is divisible by 3.
Step 4: For divisibility by 13, use the rule: Multiply the last digit by 9 and subtract it from the rest of the number. Repeat if necessary:
- Multiply 0 by 9 (0 × 9 = 0), subtract from remaining digits (156 - 0 = 156).
- Multiply last digit of 156 by 9 (6 × 9 = 54), subtract from remaining digits (15 - 54 = -39), which is divisible by 13.
The divisibility rule for 780 helps us find out if a number is divisible by 780 without using the division method. Let's check whether 1560 is divisible by 780 using this rule.
Step 1: Check divisibility by 10. The last digit of 1560 is 0, so it is divisible by 10.
Step 2: Check divisibility by 78. To do this, check divisibility by both 6 and 13, since 78 = 6 × 13.
Step 3: For divisibility by 6, check divisibility by both 2 and 3:
- 1560 is divisible by 2 because the last digit is 0 (an even number).
- Sum the digits of 1560 (1 + 5 + 6 + 0 = 12), which is divisible by 3.
Step 4: For divisibility by 13, use the rule: Multiply the last digit by 9 and subtract it from the rest of the number. Repeat if necessary:
- Multiply 0 by 9 (0 × 9 = 0), subtract from remaining digits (156 - 0 = 156).
- Multiply last digit of 156 by 9 (6 × 9 = 54), subtract from remaining digits (15 - 54 = -39), which is divisible by 13.
Tips and Tricks for Divisibility Rule of 780
Understanding divisibility rules can help students master division. Here are some tips and tricks for the divisibility rule of 780:
Know the factors of 780: Memorize the factorization (780 = 2 × 3 × 5 × 13) to quickly check divisibility.
Use negative numbers: If the subtraction yields a negative result, treat it as positive for checking divisibility.
Repeat the process for large numbers: Continue applying the divisibility rules until reaching a small enough number to verify divisibility.
Use the division method to verify: Use division as a way to cross-check results and reinforce learning.
Common Mistakes and How to Avoid Them in Divisibility Rule of 780
The divisibility rule of 780 helps us quickly check if a number is divisible by 780, but common mistakes can occur. Here are some common errors and how to avoid them:
Mistake 1
Not following the correct steps.
Follow all steps, including checking divisibility by 10, 6, and 13.
Divisibility Rule of 780 Examples
Problem 1
Is 2340 divisible by 780?
Yes, 2340 is divisible by 780.
Explanation
To check if 2340 is divisible by 780, we need to see if it meets the divisibility rules for 2, 3, 5, and 13 (since 780 = 2 x 3 x 5 x 13).
1) 2340 ends in 0, so it is divisible by 2.
2) The sum of the digits (2 + 3 + 4 + 0 = 9) is divisible by 3.
3) 2340 ends in 0, so it is divisible by 5.
4) Divide 2340 by 13, and we get 180, which is an integer.
Since 2340 is divisible by 2, 3, 5, and 13, it is divisible by 780.
Problem 2
Check the divisibility rule of 780 for 7800.
Yes, 7800 is divisible by 780.
Explanation
To check if 7800 is divisible by 780, verify divisibility by 2, 3, 5, and 13.
1) 7800 ends in 0, so it is divisible by 2.
2) The sum of the digits (7 + 8 + 0 + 0 = 15) is divisible by 3.
3) 7800 ends in 0, so it is divisible by 5.
4) Divide 7800 by 13, and we get 600, which is an integer.
Since 7800 is divisible by 2, 3, 5, and 13, it is divisible by 780.
Problem 3
Is -1560 divisible by 780?
Yes, -1560 is divisible by 780.
Explanation
To check divisibility of -1560 by 780, we check the positive number.
1) 1560 ends in 0, so it is divisible by 2.
2) The sum of the digits (1 + 5 + 6 + 0 = 12) is divisible by 3.
3) 1560 ends in 0, so it is divisible by 5.
4) Divide 1560 by 13, and we get 120, which is an integer.
Since 1560 is divisible by 2, 3, 5, and 13, it is divisible by 780.
Problem 4
Can 1456 be divisible by 780 following the divisibility rule?
No, 1456 is not divisible by 780.
Explanation
To check if 1456 is divisible by 780, verify divisibility by 2, 3, 5, and 13.
1) 1456 ends in 6, so it is divisible by 2.
2) The sum of the digits (1 + 4 + 5 + 6 = 16) is not divisible by 3.
Since 1456 is not divisible by 3, it is not divisible by 780.
Problem 5
Check the divisibility rule of 780 for 3120.
Yes, 3120 is divisible by 780
Explanation
To check if 3120 is divisible by 780, verify divisibility by 2, 3, 5, and 13.
1) 3120 ends in 0, so it is divisible by 2.
2) The sum of the digits (3 + 1 + 2 + 0 = 6) is divisible by 3.
3) 3120 ends in 0, so it is divisible by 5.
4) Divide 3120 by 13, and we get 240, which is an integer.
Since 3120 is divisible by 2, 3, 5, and 13, it is divisible by 780.
FAQs on Divisibility Rule of 780
1.What is the divisibility rule for 780?
2.How many numbers between 1 and 1000 are divisible by 780?
3. Is 2340 divisible by 780
4.What if I get 0 after subtracting?
5.How can children in United States use numbers in everyday life to understand Divisibility Rule of 780?
6.What are some fun ways kids in United States can practice Divisibility Rule of 780 with numbers?
7.What role do numbers and Divisibility Rule of 780 play in helping children in United States develop problem-solving skills?
8.How can families in United States create number-rich environments to improve Divisibility Rule of 780 skills?
Important Glossaries for Divisibility Rule of 780
- Divisibility rule: A set of rules to determine if a number is divisible by another number without performing division.
- Factors: Numbers that multiply together to produce another number. For example, 780 = 2 × 3 × 5 × 13.
- Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 780 are 780, 1560, 2340, etc.
- Integers: Whole numbers, including positive, negative numbers, and zero.
- Subtraction: The process of finding the difference between two numbers by reducing one from another.
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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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