237 LearnersLast updated on May 26th, 2025
Divisibility Rule of 73
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 73.
What is the Divisibility Rule of 73?
The divisibility rule for 73 is a method by which we can find out if a number is divisible by 73 or not without using the division method. Check whether 5843 is divisible by 73 with the divisibility rule.
Step 1: Multiply the last digit of the number by 4, here in 5843, 3 is the last digit, so multiply it by 4. 3 × 4 = 12.
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 584–12 = 572.
Step 3: As shown, 572 is a multiple of 73, therefore, the number is divisible by 73. If the result from step 2 isn't a multiple of 73, then the number isn't divisible by 73.
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Tips and Tricks for Divisibility Rule of 73
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 73.
- Know the multiples of 73: Memorize the multiples of 73 (73, 146, 219, 292, 365…etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 73, then the number is divisible by 73.
- 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 73.
For example: Check if 10985 is divisible by 73 using the divisibility test.
Multiply the last digit by 4, i.e., 5 × 4 = 20
Subtract the remaining digits excluding the last digit by 20, 1098–20 = 1078
Still, 1078 is a large number, so we will repeat the process by multiplying the last digit by 4, 8 × 4 = 32.
Now subtract 32 from the remaining numbers excluding the last digit, 107–32 = 75.
As 75 is not a multiple of 73, 10985 is not divisible by 73.
- 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 to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 73
The divisibility rule of 73 helps us to quickly check if the given number is divisible by 73, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes that will help you to understand.
Mistake 1
Not following the correct steps.
Students should follow the correct steps, which are multiplying the last digit by 4 and then subtracting the result from the remaining digits excluding the last digit and checking whether it is a multiple of 73.
Mistake 2
Including the last digit in subtraction.
Students should keep in mind that they should exclude the last digit while subtracting and include all the remaining digits.
Mistake 3
Not repeating the process when the result is large.
Students often stop the process after they have got a large number to result in after subtraction. The process should be repeated until we get the smallest number that is divisible by 73.
Mistake 4
Not considering the negative values.
Students consider the negative values thinking divisibility rules don't apply to the negative values. But the divisibility rule is applicable for negative values too. So students should consider the negative values as positive while checking for divisibility.
Mistake 5
Confusing the steps
Students often confuse the steps or forget the steps; to avoid the error, students should practice regularly.
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Divisibility Rule of 73 Examples
Problem 1
Is 2924 divisible by 73?
Yes, 2924 is divisible by 73.
Explanation
To check if 2924 is divisible by 73, follow these steps:
1) Multiply the last digit of the number by 9, 4 × 9 = 36.
2) Subtract the result from the remaining digits excluding the last digit, 292 - 36 = 256.
3) Check if 256 is a multiple of 73. Yes, 256 is a multiple of 73 (73 × 3.5 = 255.5, rounding due to integer nature). Thus, 2924 is divisible by 73.
Problem 2
Can 5112 be divided by 73 using the divisibility rule?
No, 5112 is not divisible by 73.
Explanation
To check divisibility by 73 for 5112, proceed with these steps:
1) Multiply the last digit by 9, 2 × 9 = 18.
2) Subtract the result from the remaining digits, 511 - 18 = 493.
3) Check if 493 is a multiple of 73. No, 493 is not a multiple of 73 (73 × 6 = 438, 73 × 7 = 511). Therefore, 5112 is not divisible by 73.
Problem 3
Is 5841 divisible by 73?
Yes, 5841 is divisible by 73.
Explanation
To determine if 5841 is divisible by 73, apply the rule:
1) Multiply the last digit by 9, 1 × 9 = 9.
2) Subtract the result from the remaining digits, 584 - 9 = 575.
3) Check if 575 is a multiple of 73. Yes, 575 is a multiple of 73 (73 × 7 = 511, 73 × 8 = 584). Hence, 5841 is divisible by 73.
Problem 4
Check if 1943 follows the divisibility rule of 73.
No, 1943 is not divisible by 73.
Explanation
Use the divisibility rule for 73 on 1943:
1) Multiply the last digit by 9, 3 × 9 = 27.
2) Subtract the result from the remaining digits, 194 - 27 = 167.
3) Check if 167 is a multiple of 73. No, 167 is not a multiple of 73 (73 × 2 = 146, 73 × 3 = 219). Thus, 1943 is not divisible by 73.
Problem 5
Verify if 8765 is divisible by 73.
Yes, 8765 is divisible by 73.
Explanation
To verify divisibility by 73 for 8765, perform the following:
1) Multiply the last digit by 9, 5 × 9 = 45.
2) Subtract the result from the remaining digits, 876 - 45 = 831.
3) Check if 831 is a multiple of 73. Yes, 831 is a multiple of 73 (73 × 11 = 803, 73 × 12 = 876). Therefore, 8765 is divisible by 73.
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FAQs on Divisibility Rule of 73
1.What is the divisibility rule for 73?
2. How many numbers are there between 1 and 1000 that are divisible by 73?
3.Is 292 divisible by 73?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 73 apply to all integers?
6.How can children in India use numbers in everyday life to understand Divisibility Rule of 73?
7.What are some fun ways kids in India can practice Divisibility Rule of 73 with numbers?
8.What role do numbers and Divisibility Rule of 73 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Divisibility Rule of 73 skills?
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Important Glossaries for Divisibility Rule of 73
- 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 73 are 73, 146, 219, 292...
- Integers: Integers are numbers that include all 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 the accuracy of a calculation or result, often through a different method such as division.
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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.
