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.
 

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.

• 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.