Divisibility Rule of 731

The divisibility rule for 731 is a method by which we can find out if a number is divisible by 731 without using the division method. Here is an example to check whether 2193 is divisible by 731 using the divisibility rule.

Step 1: Multiply the last digit of the number by 2. In 2193, 3 is the last digit, so multiply it by 2. 3 × 2 = 6.

Step 2: Subtract the result from Step 1 from the remaining values without including the last digit. i.e., 219–6 = 213.

Step 3: As 213 is not a multiple of 731, 2193 is not divisible by 731. If the result from Step 2 were a multiple of 731, the number would be divisible by 731.

Learning divisibility rules will help kids master division. Let's learn a few tips and tricks for the divisibility rule of 731.

Know the multiples of 731:

Memorize the multiples of 731 (731, 1462, 2193, ... etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 731, then the number is divisible by 731.

Use negative numbers:

If the result we get after subtraction is negative, we will consider the absolute value for checking divisibility.

Repeat the process for large numbers:

Students should repeat the divisibility process until they reach a smaller number to check divisibility by 731. For example, to check if 4386 is divisible by 731, multiply the last digit by 2, i.e., 6 × 2 = 12. Subtract the remaining digits excluding the last digit by 12, 438–12 = 426. As 426 is not a multiple of 731, 4386 is not divisible by 731.

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.

• Divisibility Rule: The set of rules used to find out whether a number is divisible by another number without performing division.
   
• Multiples: The results obtained after multiplying a number by an integer. For example, multiples of 731 are 731, 1462, 2193, etc.
   
• Integers: Numbers that include all whole numbers, negative numbers, and zero.
   
• Subtraction: A 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.