173 LearnersLast updated on May 26th, 2025
Divisibility Rule of 689
The divisibility rule is a way to determine whether a number is divisible by another number without using the division method. In real life, we can use divisibility rules for quick math, dividing things evenly, and sorting things. In this topic, we will learn about the divisibility rule of 689.
What is the Divisibility Rule of 689?
The divisibility rule for 689 is a method by which we can find out if a number is divisible by 689 without using the division method. Check whether 1378 is divisible by 689 with the divisibility rule.
Step 1: Multiply the last digit of the number by 2. In 1378, 8 is the last digit, so multiply it by 2. 8 × 2 = 16.
Step 2: Subtract the result from Step 1 from the remaining values, but do not include the last digit. i.e., 137–16 = 121.
Step 3: Since 121 is not a multiple of 689, the number is not divisible by 689. If the result from Step 2 were a multiple of 689, then the number would be divisible by 689.
Tips and Tricks for Divisibility Rule of 689
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 689.
- Know the multiples of 689: Memorize the multiples of 689 (689, 1378, 2067, ...) to quickly check divisibility. If the result from the subtraction is a multiple of 689, then the number is divisible by 689.
- Use the negative numbers: If the result we get after the subtraction is negative, consider its absolute value for checking divisibility.
- Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by 689.
For example, check if 2756 is divisible by 689 using the divisibility test. Multiply the last digit by 2, i.e., 6 × 2 = 12.
Subtract 12 from the remaining digits excluding the last digit, 275–12 = 263. Since 263 is still a large number, repeat the process. Multiply the last digit by 2, 3 × 2 = 6.
Subtracting 6 from the remaining numbers excluding the last digit, 26–6 = 20. Since 20 is not a multiple of 689, 2756 is not divisible by 689.
- 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 689
The divisibility rule of 689 helps us to quickly check if a given number is divisible by 689, 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 following the correct steps.
Students should follow the correct steps: multiply the last digit by 2, subtract the result from the remaining digits excluding the last digit, and check whether it is a multiple of 689.
Divisibility Rule of 689 Examples
Problem 1
Is 2067 divisible by 689?
Yes, 2067 is divisible by 689.
Explanation
To determine if 2067 is divisible by 689, we can use the following method:
1) Split the number into groups of three digits from right to left. Since 2067 is less than 1000, we only have one group: 2067.
2) Calculate 2067 ÷ 689 = 3.
3) Since the result is an integer with no remainder, 2067 is divisible by 689.
Problem 2
Check the divisibility rule of 689 for 1378.
No, 1378 is not divisible by 689.
Explanation
To check if 1378 is divisible by 689:
1) Split the number into groups of three digits from right to left. Since 1378 is less than 1000, we only have one group: 1378.
2) Calculate 1378 ÷ 689 ≈ 2.
3) Since the result is not an integer and has a remainder, 1378 is not divisible by 689.
Problem 3
Is -3445 divisible by 689?
No, -3445 is not divisible by 689.
Explanation
To check if -3445 is divisible by 689:
1) Remove the negative sign and consider the positive number 3445.
2) Split the number into groups of three digits from right to left. Since 3445 is less than 1000, we have one group: 3445.
3) Calculate 3445 ÷ 689 ≈ 5.
4) Since the result is not an integer and has a remainder, 3445 is not divisible by 689.
Problem 4
Can 689 be divisible by 689 following the divisibility rule?
Yes, 689 is divisible by 689.
Explanation
To check if 689 is divisible by itself:
1) Split the number into groups of three digits from right to left, which is just 689 itself.
2) Calculate 689 ÷ 689 = 1.
3) Since the result is exactly 1, 689 is divisible by 689.
Problem 5
Check the divisibility rule of 689 for 6890.
No, 6890 is not divisible by 689.
Explanation
To check if 6890 is divisible by 689:
1) Split the number into groups of three digits from right to left, giving us two groups: 6 and 890.
2) Calculate 6890 ÷ 689 ≈ 10.
3) Since the result is not an integer and has a remainder, 6890 is not divisible by 689.
FAQs on Divisibility Rule of 689
1.What is the divisibility rule for 689?
2.How many numbers between 1 and 10000 are divisible by 689?
3.Is 4134 divisible by 689?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 689 apply to all integers?
6.How can children in Australia use numbers in everyday life to understand Divisibility Rule of 689?
7.What are some fun ways kids in Australia can practice Divisibility Rule of 689 with numbers?
8.What role do numbers and Divisibility Rule of 689 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Divisibility Rule of 689 skills?
Important Glossary for Divisibility Rule of 689
- Divisibility rule: A set of rules used to determine whether a number is divisible by another number without direct division.
- Multiples: The results we get after multiplying a number by an integer. For example, multiples of 689 are 689, 1378, 2067, ...
- Integers: Numbers that include all whole numbers, negative numbers, and zero.
- Subtraction: The process of finding the difference between two numbers by reducing one number from another.
- Absolute value: The non-negative value of a number without regard to its sign. For example, the absolute value of -20 is 20.
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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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