Divisibility Rule of 667
2026-02-28 10:38 Diff
https://brightchamps.com/en-us/math/numbers/divisibility-rule-of-667

313 Learners

Last updated on August 5, 2025

The divisibility rule is a method to determine 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 667.

What is the Divisibility Rule of 667?

The divisibility rule for 667 is a method by which we can find out if a number is divisible by 667 or not without using the division method. Check whether 2001 is divisible by 667 with the divisibility rule.

Step 1: Divide the number into groups of three digits from the right. For 2001, we have groups: 001 and 2.

Step 2: Subtract the group 667 times the integer part of the division of the left group by 667 from the right group. Here, 001 - (667 × 0) = 1.

Step 3: As the result is not zero or 667, 2001 is not divisible by 667.

Tips and Tricks for Divisibility Rule of 667

Learning the divisibility rule will help learners master division. Let’s learn a few tips and tricks for the divisibility rule of 667.

  • Know the multiples of 667: Memorize the multiples of 667 (667, 1334, 2001, 2668, etc.) to quickly check the divisibility. If the result from the subtraction is either zero or a multiple of 667, then the number is divisible by 667.
     
  • Use the negative numbers: If the result we get after the subtraction is negative, consider its absolute value when checking divisibility.
     
  • Repeat the process for large numbers: Continue the divisibility process until reaching a small number that can be easily checked against 667. For example: Check if 5334 is divisible by 667 using the divisibility test. Divide 5334 into groups of three digits: 334 and 5. Subtract 334 - (667 × 0) = 334, which is not zero or 667. Hence, 5334 is not divisible by 667.
     
  • Use the division method to verify: Learners can use the division method as a way to verify and crosscheck their results. This helps in verification and learning.

Common Mistakes and How to Avoid Them in Divisibility Rule of 667

The divisibility rule of 667 helps us quickly check if a given number is divisible by 667, but common mistakes like calculation errors can lead to incorrect results. Here we will understand some common mistakes and how to avoid them.

Explore Our Programs

Download Worksheets

Problem 1

Is 2001 divisible by 667?

Okay, lets begin

Yes, 2001 is divisible by 667.

Explanation

To verify if 2001 is divisible by 667, perform the following steps:


1) Divide the number by 667: 2001 ÷ 667 = 3


2) Check if the quotient is a whole number. Yes, 3 is a whole number, indicating 2001 is divisible by 667.

Well explained 👍

Problem 2

Check the divisibility rule of 667 for 4002.

Okay, lets begin

Yes, 4002 is divisible by 667.

Explanation

To check if 4002 is divisible by 667, follow these steps:


1) Divide the number by 667: 4002 ÷ 667 = 6.


2) Verify if the quotient is a whole number. Yes, 6 is a whole number, confirming that 4002 is divisible by 667.

Well explained 👍

Problem 3

Is 1334 divisible by 667?

Okay, lets begin

Yes, 1334 is divisible by 667.

Explanation

To determine if 1334 is divisible by 667, use the following method:


1) Divide the number by 667: 1334 ÷ 667 = 2.


2) Ensure the quotient is a whole number. Yes, 2 is a whole number, so 1334 is divisible by 667.

Well explained 👍

Problem 4

Can 1000 be divisible by 667 following the divisibility rule?

Okay, lets begin

No, 1000 is not divisible by 667.

Explanation

To verify if 1000 is divisible by 667, follow these steps:


1) Divide the number by 667: 1000 ÷ 667 ≈ 1.5.


2) Check if the quotient is a whole number. No, 1.5 is not a whole number, indicating 1000 is not divisible by 667.

Well explained 👍

Problem 5

Check the divisibility rule of 667 for 6003.

Okay, lets begin

Yes, 6003 is divisible by 667.

Explanation

To check if 6003 is divisible by 667, perform the following:


1) Divide the number by 667: 6003 ÷ 667 = 9.


2) Verify that the quotient is a whole number. Yes, 9 is a whole number, confirming that 6003 is divisible by 667.

Well explained 👍

FAQs on Divisibility Rule of 667

1.What is the divisibility rule for 667?

The divisibility rule for 667 involves dividing the number into groups of three digits from the right, subtracting the group 667 times the integer part of the division of the left group by 667 from the right group, and checking if the result is zero or a multiple of 667.

2.How many numbers are there between 1 and 2000 that are divisible by 667?

There are 3 numbers divisible by 667 between 1 and 2000. The numbers are 667, 1334, and 2001.

3.Is 1334 divisible by 667?

Yes, because 1334 is a multiple of 667 (667 × 2 = 1334).

4.What if I get 0 after subtraction?

If you get 0 after subtraction, the number is divisible by 667.

5.Does the divisibility rule of 667 apply to all integers?

Yes, the divisibility rule of 667 applies to all integers.

Important Glossaries for Divisibility Rule of 667

  • Divisibility rule: Guidelines to determine if a number is divisible by another number without actual division.
     
  • Multiples: The results obtained by multiplying a number by integers. For example, multiples of 667 are 667, 1334, 2001, etc.
     
  • Integer: A whole number that can be positive, negative, or zero.
     
  • Subtraction: Finding the difference between two numbers by deducting one from another.
     
  • Absolute value: The non-negative value of a number without regard to its sign.

What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math

▶

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.