Divisibility Rule of 103

The divisibility rule for 103 is a method by which we can find out if a number is divisible by 103 or not without using the division method. Check whether 2060 is divisible by 103 with the divisibility rule.
 

Step 1: Break the number into blocks of three from the right. Here, in 2060, you have 060 and 2 (consider 2 as 002 for the purpose of the rule).
 

Step 2: Multiply the block on the furthest right by 1, the next block by 10, and so on in increasing powers of 10. In this example, it would be 060 × 1 + 002 × 10 = 60 + 20 = 80.
 

Step 3: Check if the sum is a multiple of 103. In this case, 80 is not a multiple of 103, so 2060 is not divisible by 103.

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 103.
 

• Know the multiples of 103: Memorize the multiples of 103 (103, 206, 309, etc.) to quickly check divisibility. If the result from the sum is a multiple of 103, then the number is divisible by 103.
   
• Use consistent block sizes: Ensure each block is of three digits. If necessary, prepend zeros to make it a three-digit block.
   
• Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number. For example, check if 30909 is divisible by 103. Break it into blocks: 909 and 030. Compute: 909 × 1 + 030 × 10 = 909 + 300 = 1209. 1209 is large, so repeat: 209 and 001, which leads to 209 + 10 = 219. Since 219 is a multiple of 103, 30909 is divisible by 103.
   
• 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 verify and also learn.
   

• Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not. For example, a number is divisible by 2 if the number ends with an even number.
   
• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 103 are 103, 206, 309, etc.
   
• Blocks: Groups of digits, usually three, used in the divisibility rule for larger numbers.
   
• Powers of 10: The sequence of multipliers (1, 10, 100, etc.) used in the divisibility rule.
   
• Sum: The result obtained by adding numbers together, used to determine if a number is divisible by 103.