Divisibility Rule of 377
2026-02-28 10:32 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 performing actual division. In real life, we use divisibility rules for quick calculations, evenly dividing things, and sorting items. In this topic, we will learn about the divisibility rule of 377.

What is the Divisibility Rule of 377?

The divisibility rule for 377 is a method to check if a number is divisible by 377 without performing division. Let's check whether 75429 is divisible by 377 using the divisibility rule.
 

Step 1: Separate the last three digits of the number, here in 75429, which are 429.

Step 2: Subtract the number formed by the last three digits from the rest of the number multiplied by 3. In this case, multiply 75 by 3: 75 × 3 = 225.

Step 3: Subtract 225 from 429: 429 - 225 = 204.

Step 4: Since 204 is not a multiple of 377, 75429 is not divisible by 377. If the result from Step 3 were a multiple of 377, then the number would be divisible by 377.

Tips and Tricks for Divisibility Rule of 377

Learning the divisibility rule can help students master division. Here are a few tips and tricks for the divisibility rule of 377.
 

Know the multiples of 377:

Memorize the multiples of 377 (377, 754, 1131, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 377, then the number is divisible by 377.

Use negative numbers:

If the result after subtraction is negative, consider it as positive when checking divisibility.
 

Repeat the process for large numbers: 

Continue the divisibility process until you reach a small number that is easier to check for divisibility by 377.

For example, check if 150754 is divisible by 377: Separate the last three digits, 754, and multiply the rest by 3: 150 × 3 = 450.

Subtract 450 from 754: 754 - 450 = 304. Since 304 is not a multiple of 377, 150754 is not divisible by 377.

Use the division method to verify:

Verify and cross-check results using division. It helps confirm findings and aids in learning.

Common Mistakes and How to Avoid Them in Divisibility Rule of 377

The divisibility rule of 377 helps quickly check if a number is divisible by 377, but common mistakes can lead to incorrect results. Here are some common mistakes and solutions:
 

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Problem 1

Is 754 divisible by 377?

Okay, lets begin

No, 754 is not divisible by 377.
 

Explanation

To check if 754 is divisible by 377, we need to use the divisibility rule for 377 (hypothetical). 

1) Assume the rule states to multiply the last two digits by a certain factor and subtract the result from the remaining number. 

2) Here, multiply the last two digits (54) by 3, giving 162.

3) Subtract this from the remaining digits (7), leading to -155.

4) Since -155 is not a multiple of 377, 754 is not divisible by 377.

Well explained 👍

Problem 2

Check the divisibility rule of 377 for 1131.

Okay, lets begin

Yes, 1131 is divisible by 377.

Explanation

Assuming a rule for 377, let's check:

1) Multiply the last two digits (31) by 3, resulting in 93.

2) Subtract the result from the remaining number (11), which gives -82.

3) Check if -82 plus a multiple of 377 equals zero. Indeed, 1131 divided by 377 is exactly 3, making it divisible.

Well explained 👍

Problem 3

Is 2262 divisible by 377?

Okay, lets begin

Yes, 2262 is divisible by 377.

Explanation

Following the hypothetical rule for 377:

1) Multiply the last two digits (62) by 3, resulting in 186.

2) Subtract the result from the remaining number (22), which gives -164.

3) Verify if adding a multiple of 377 to this results in zero. Indeed, 2262 divided by 377 is exactly 6.

Well explained 👍

Problem 4

Can 1890 be divisible by 377 following the divisibility rule?,Check the divisibility rule of 377 for 754.

Okay, lets begin

No, 1890 isn't divisible by 377.
 

,No, 754 is not divisible by 377.

Explanation

To check using the hypothetical rule:

1) Multiply the last two digits (90) by 3, resulting in 270.

2) Subtract the result from the remaining digits (18), which gives -252.

3) Since -252 plus no integer multiple of 377 equals zero, 1890 is not divisible by 377.

Assuming the rule:

1) Multiply the last two digits (54) by 3, giving 162.

2) Subtract the result from the remaining number (7), leading to -155.

3) Since -155 is not a multiple of 377, 754 is not divisible by 377.

Well explained 👍

FAQs on Divisibility Rule of 377

1.What is the divisibility rule for 377?

The divisibility rule for 377 involves separating the last three digits, multiplying the rest by 3, and subtracting this product from the last three digits to check if the result is a multiple of 377.

2.How many numbers are there between 1 and 2000 that are divisible by 377?

There are 5 numbers divisible by 377 between 1 and 2000. They are 377, 754, 1131, 1508, and 1885.

3.Is 754 divisible by 377?

Yes, because 754 is a multiple of 377 (377 × 2 = 754).

4.What if I get 0 after subtracting?

If you get 0, the number is divisible by 377.
 

5.Does the divisibility rule of 377 apply to all integers?

Yes, the divisibility rule of 377 applies to all integers.
 

Important Glossaries for Divisibility Rule of 377

  • Divisibility rule: A set of rules to find out if one number is divisible by another without direct division.
  • Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 377 are 377, 754, 1131, etc.
  • Integers: Whole numbers including negative numbers and zero.
  • Subtraction: The process of finding the difference between two numbers by reducing one from another.
  • Verification: The process of confirming the correctness of a result, often through alternative methods like division.

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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.