Divisibility Rule of 457

The divisibility rule for 457 is a method by which we can find out if a number is divisible by 457 or not without using the division method. Check whether 914 is divisible by 457 with the divisibility rule.

Step 1: Multiply the last digit of the number by 3. Here in 914, 4 is the last digit, so multiply it by 3. 4 × 3 = 12.

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 91–12 = 79.

Step 3: As it is shown that 79 is not a multiple of 457, the number is not divisible by 457. If the result from Step 2 were a multiple of 457, then the number would be divisible by 457.

Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 457.

• Know the multiples of 457: Memorize the multiples of 457 (457, 914, 1371, 1828, etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 457, then the number is divisible by 457.
   
• Use the negative numbers: If the result we get after the subtraction is negative, we will avoid the symbol and consider it as positive for checking the divisibility of a number.
   
• Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by 457. For example: Check if 4572 is divisible by 457 using the divisibility test. Multiply the last digit by 3, i.e., 2 × 3 = 6. Subtract the remaining digits excluding the last digit by 6, 457–6 = 451. Still, 451 is not a large number, but let's repeat the steps for clarity. Multiply the last digit of 451 by 3, 1 × 3 = 3. Now subtracting 3 from the remaining numbers excluding the last digit, 45–3 = 42. As 42 is not a multiple of 457, 4572 is not divisible by 457.
   
• Use the division method to verify: Students can use the division method as a way to verify and crosscheck their results. This will help them verify and also learn.

• Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not. 
   
• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 457 are 457, 914, 1371, etc.
   
• Integers: Integers are numbers that include all the whole numbers, negative numbers, and zero.
   
• Subtraction: Subtraction is a process of finding out the difference between two numbers by reducing one number from another.
   
• Verification: Verification is the process of confirming that a result or calculation is correct by using another method, such as division.