Divisibility Rule of 689
2026-02-28 13:03 Diff
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Last updated on August 5, 2025

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.
 

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Problem 1

Is 2067 divisible by 689?

Okay, lets begin

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.

Well explained 👍

Problem 2

Check the divisibility rule of 689 for 1378.

Okay, lets begin

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.

Well explained 👍

Problem 3

Is -3445 divisible by 689?

Okay, lets begin

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.

Well explained 👍

Problem 4

Can 689 be divisible by 689 following the divisibility rule?

Okay, lets begin

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.

Well explained 👍

Problem 5

Check the divisibility rule of 689 for 6890.

Okay, lets begin

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.

Well explained 👍

FAQs on Divisibility Rule of 689

1.What is the divisibility rule for 689?

The divisibility rule for 689 involves multiplying the last digit by 2, subtracting the result from the remaining digits excluding the last digit, and checking if the result is a multiple of 689.

2.How many numbers between 1 and 10000 are divisible by 689?

There are 14 numbers between 1 and 10000 that can be divided by 689. These numbers are 689, 1378, 2067, 2756, 3445, 4134, 4823, 5512, 6201, 6890, 7579, 8268, 8957, 9646.

3.Is 4134 divisible by 689?

Yes, because 4134 is a multiple of 689 (689 × 6 = 4134).

4.What if I get 0 after subtracting?

If you get 0 after subtracting, it is considered that the number is divisible by 689.

5.Does the divisibility rule of 689 apply to all integers?

Yes, the divisibility rule of 689 applies to all integers.

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

: She loves to read number jokes and games.