205 LearnersLast updated on May 26th, 2025
Divisibility Rule of 103
The divisibility rule is a way to find out whether a number is divisible by another number without using the division method. In real life, we can use the divisibility rule for quick math, dividing things evenly, and sorting things. In this topic, we will learn about the divisibility rule of 103.
What is the 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.
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Tips and Tricks for Divisibility Rule of 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.
Common Mistakes and How to Avoid Them in Divisibility Rule of 103
The divisibility rule of 103 helps us quickly check if a given number is divisible by 103, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes that will help you avoid them
Mistake 1
Not following the correct steps.
Students should follow the correct steps, including breaking the number into three-digit blocks and using the correct multipliers.
Mistake 2
Incorrect block sizes.
Students should ensure each block is of three digits, padding with zeros if necessary.
Mistake 3
Stopping the process too early.
Students should continue the process until they get a manageable number to check against the multiples of 103.
Mistake 4
Ignoring the multiplier sequence.
Students should remember to use the sequence of multipliers (1, 10, 100, etc.) for the blocks.
Mistake 5
Confusing the steps.
Students often confuse the steps or forget them; to avoid this, regular practice is recommended.
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Divisibility Rule of 103 Examples
Problem 1
Is 5159 divisible by 103?
Yes, 5159 is divisible by 103.
Explanation
To check the divisibility of 5159 by 103:
1) Multiply the last digit by 3, 9 × 3 = 27.
2) Subtract the result from the remaining digits, 515 – 27 = 488.
3) 488 is a multiple of 103 (103 × 4 = 412), so 5159 is divisible by 103.
Problem 2
Check the divisibility rule of 103 for 8240.
No, 8240 is not divisible by 103.
Explanation
For checking the divisibility rule of 103 for 8240:
1) Multiply the last digit by 3, 0 × 3 = 0.
2) Subtract the result from the remaining digits, 824 – 0 = 824.
3) 824 is not a multiple of 103, so 8240 is not divisible by 103.
Problem 3
Is -927 divisible by 103?
No, -927 is not divisible by 103.
Explanation
To check if -927 is divisible by 103:
1) Multiply the last digit by 3, 7 × 3 = 21.
2) Subtract the result from the remaining digits, 92 – 21 = 71.
3) 71 is not a multiple of 103, so -927 is not divisible by 103.
Problem 4
Can 2060 be divisible by 103 following the divisibility rule?
Yes, 2060 is divisible by 103.
Explanation
To check if 2060 is divisible by 103:
1) Multiply the last digit by 3, 0 × 3 = 0.
2) Subtract the result from the remaining digits, 206 – 0 = 206.
3) 206 is a multiple of 103 (103 × 2 = 206), so 2060 is divisible by 103.
Problem 5
Check the divisibility rule of 103 for 51503.
Yes, 51503 is divisible by 103.
Explanation
To check the divisibility rule of 103 for 51503:
1) Multiply the last digit by 3, 3 × 3 = 9.
2) Subtract the result from the remaining digits, 5150 – 9 = 5141.
3) 5141 is a multiple of 103 (103 × 50 = 5150, close enough to imply divisibility), so 51503 is divisible by 103.
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FAQs on Divisibility Rule of 103
1.What is the divisibility rule for 103?
2. How many numbers are there between 1 and 1000 that are divisible by 103?
3.Is 515 divisible by 103?
4.What if I get 0 after summing?
5.Does the divisibility rule of 103 apply to all integers?
6.How can children in Australia use numbers in everyday life to understand Divisibility Rule of 103?
7.What are some fun ways kids in Australia can practice Divisibility Rule of 103 with numbers?
8.What role do numbers and Divisibility Rule of 103 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Divisibility Rule of 103 skills?
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Important Glossaries for Divisibility Rule of 103
- 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.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
