Divisibility Rule of 349

The divisibility rule for 349 is a method by which we can determine if a number is divisible by 349 without using the division method. Check whether 104,747 is divisible by 349 using the divisibility rule.

Step 1: Multiply the last digit of the number by 3, here in 104,747, 7 is the last digit, so multiply it by 3. 7 × 3 = 21.

Step 2: Subtract the result from Step 1 from the remaining values, excluding the last digit. i.e., 10,474 - 21 = 10,453.

Step 3: Repeat the process until you reach a small number. Multiply the last digit by 3, i.e., 3 × 3 = 9. Subtract from the remaining number, 1,045 - 9 = 1,036.

Step 4: Repeat again. Multiply the last digit by 3, i.e., 6 × 3 = 18. Subtract from the remaining number, 103 - 18 = 85.

Step 5: If the result is a multiple of 349, then the number is divisible by 349. Here, 85 is not a multiple of 349, so 104,747 is not divisible by 349.

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 349.

Know the multiples of 349:

Memorize the multiples of 349 (349, 698, 1,047, etc.) to quickly check divisibility.

Use negative numbers:

If the result after subtraction is negative, treat it as positive for checking divisibility.

Repeat the process for large numbers:

Keep repeating the divisibility process until reaching a small number. For example, check if 698 is divisible by 349 using the divisibility test. Multiply the last digit by 3, i.e., 8 × 3 = 24. Subtract from the remaining digits, 69 - 24 = 45. Since 45 is not a multiple of 349, 698 is not divisible by 349.

Use the division method to verify:

The division method can be used to verify and cross-check results, helping with understanding.

• Divisibility rule: A set of rules used to determine if a number is divisible by another number.

• Multiples: Results obtained after multiplying a number by an integer, such as multiples of 349.

• Integers: Numbers that include all whole numbers, negative numbers, and zero.

• Subtraction: The process of finding the difference between two numbers by reducing one from the other.

• Verification: The method of confirming results, often using division to ensure accuracy.