182 LearnersLast updated on May 26th, 2025
Divisibility Rule of 770
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 770.
What is the Divisibility Rule of 770?
The divisibility rule for 770 is a method by which we can find out if a number is divisible by 770 or not without using the division method. To check whether a number is divisible by 770, it must be divisible by both 7, 11, and 10. Let's check whether 8470 is divisible by 770 using this rule.
Step 1: Check divisibility by 10. The number must end in 0. 8470 ends in 0, so it is divisible by 10.
Step 2: Check divisibility by 7. Multiply the last digit by 2, here the last digit is 0, so 0 × 2 = 0. Subtract this result from the remaining value, excluding the last digit: 847 - 0 = 847. Since 847 ÷ 7 = 121, the number is divisible by 7.
Step 3: Check divisibility by 11. Take the difference between the sum of the digits in odd positions and the sum of the digits in even positions: (8 + 7) - (4 + 0) = 15 - 4 = 11. Since 11 is divisible by 11, the number is divisible by 11.
Since 8470 is divisible by 7, 11, and 10, it is also divisible by 770.
Tips and Tricks for Divisibility Rule of 770
Understanding the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 770.
- Know the multiples of 770:
Memorize the multiples of 770 to quickly check divisibility. If a number is divisible by 7, 11, and 10, it is divisible by 770.
- Use the negative numbers:
If the result we get after checking divisibility is negative, consider it positive for checking the divisibility.
- Repeat the process for large numbers:
For large numbers, repeat the divisibility process until you simplify the number sufficiently. For example, check if 15400 is divisible by 770. It ends in 0, so it is divisible by 10.
For 1540, multiply the last digit (0) by 2, 0 × 2 = 0, and subtract from the rest: 154 - 0 = 154. Since 154 ÷ 7 = 22, it is divisible by 7. For 154, (1 + 4) - 5 = 0, which is divisible by 11, so 15400 is divisible by 770.
- Use the division method to verify:
Use the division method to verify and cross-check your results for better accuracy.
Common Mistakes and How to Avoid Them in Divisibility Rule of 770
The divisibility rule of 770 helps us quickly check if a given number is divisible by 770, but common mistakes like calculation errors lead to incorrect conclusions. Here we'll understand some common mistakes and how to avoid them.
Mistake 1
Not following the correct steps.
Follow the steps correctly by checking divisibility by 7, 11, and 10.
Divisibility Rule of 770 Examples
Problem 1
Is 1540 divisible by 770?
Yes, 1540 is divisible by 770.
Explanation
To determine if 1540 is divisible by 770, we need to check divisibility by both 7, 11, and 10, as 770 = 7 x 11 x 10.
1) Check divisibility by 10: The number ends in 0, so it's divisible by 10.
2) Check divisibility by 11: Alternating sum of digits is 1 - 5 + 4 - 0 = 0, which is divisible by 11.
3) Check divisibility by 7: Multiply last digit (0) by 2, subtract from rest (154) to get 154, check further: 15 - 8 = 7, which is divisible by 7.
Therefore, 1540 is divisible by 770.
Problem 2
Check if 8470 is divisible by 770.
Yes, 8470 is divisible by 770.
Explanation
To verify divisibility by 770, check divisibility by 7, 11, and 10.
1) Divisibility by 10: Ends in 0, divisible by 10.
2) Divisibility by 11: Alternating sum is 8 - 4 + 7 - 0 = 11, divisible by 11.
3) Divisibility by 7: Last digit (0) x 2 = 0, 847 - 0 = 847. Repeat: 84 - 14 = 70, which is divisible by 7.
Hence, 8470 is divisible by 770.
Problem 3
Is 3080 divisible by 770?
No, 3080 is not divisible by 770.
Explanation
We must check divisibility by 7, 11, and 10.
1) Divisibility by 10: Ends in 0, divisible by 10.
2) Divisibility by 11: Alternating sum is 3 - 0 + 8 - 0 = 11, divisible by 11.
3) Divisibility by 7: Last digit (0) x 2 = 0, 308 - 0 = 308. 30 - 16 = 14, which is divisible by 7.
However, the initial steps showed divisibility by all components, revealing an error in factorization. Re-evaluate: 308 is not divisible by 7.
Therefore, 3080 is not divisible by 770.
Problem 4
Verify divisibility of 7700 by 770.
Yes, 7700 is divisible by 770.
Explanation
Check divisibility by 7, 11, and 10.
1) Divisibility by 10: Ends in 0, divisible by 10.
2) Divisibility by 11: Alternating sum is 7 - 7 + 0 - 0 = 0, divisible by 11.
3) Divisibility by 7: Last digit (0) x 2 = 0, 770 - 0 = 770. Repeat: 77 - 0 = 77, divisible by 7.
Therefore, 7700 is divisible by 770.
Problem 5
Is 5390 divisible by 770?
No, 5390 is not divisible by 770.
Explanation
Check divisibility by 7, 11, and 10.
1) Divisibility by 10: Ends in 0, divisible by 10.
2) Divisibility by 11: Alternating sum is 5 - 3 + 9 - 0 = 11, divisible by 11.
3) Divisibility by 7: Last digit (0) x 2 = 0, 539 - 0 = 539. 53 - 18 = 35, not divisible by 7.
Therefore, 5390 is not divisible by 770.
FAQs on Divisibility Rule of 770
1.What is the divisibility rule for 770?
2.How many numbers are there between 1 and 1000 that are divisible by 770?
3.Is 2310 divisible by 770?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 770 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 770?
7.What are some fun ways kids in United States can practice Divisibility Rule of 770 with numbers?
8.What role do numbers and Divisibility Rule of 770 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 770 skills?
Glossary for Divisibility Rule of 770
- Divisibility rule: The set of rules used to determine if a number is divisible by another number without performing division.
- Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 770 are 770, 1540, 2310, etc.
- Integers: Numbers that include all whole numbers, negative numbers, and zero.
- Subtraction: The process of finding the difference between two numbers by reducing one from the other.
- Simplification: The process of reducing a number or expression to its simplest form.
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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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