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107 LearnersLast updated on March 29th, 2025
Divisibility Rule of 973
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 973.
What is the Divisibility Rule of 973?
The divisibility rule for 973 is a method by which we can find out if a number is divisible by 973 or not without using the division method. Check whether 1946 is divisible by 973 with the divisibility rule.
Step 1: Multiply the last digit of the number by 4. Here in 1946, 6 is the last digit, so multiply it by 4. 6 × 4 = 24.
Step 2: Subtract the result from Step 1 from the remaining values, but do not include the last digit. i.e., 194 - 24 = 170.
Step 3: As it is shown that 170 is not a multiple of 973, the number is not divisible by 973. If the result from Step 2 were a multiple of 973, then the number would be divisible by 973.
Tips and Tricks for Divisibility Rule of 973
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 973.
Know the multiples of 973:
Memorize the multiples of 973 (973, 1946, 2919, etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 973, then the number is divisible by 973.
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 973. For example, check if 3888 is divisible by 973 using the divisibility test. Multiply the last digit by 4, i.e., 8 × 4 = 32. Subtract 32 from the remaining digits excluding the last digit, 388 - 32 = 356. 356 is still not small enough, so repeat the process again. Multiply the last digit by 4, 6 × 4 = 24. Subtract 24 from the remaining numbers excluding the last digit, 35 - 24 = 11. As 11 is not a multiple of 973, 3888 is not divisible by 973.
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.
Common Mistakes and How to Avoid Them in Divisibility Rule of 973
The divisibility rule of 973 helps us to quickly check if the given number is divisible by 973, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes that will help you to avoid them.
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 973.
Divisibility Rule of 973 Examples
Problem 1
Is 1946 divisible by 973?
Yes, 1946 is divisible by 973.
Explanation
To check divisibility by 973, follow these steps:
1) Double the last three digits of the number: 946 × 2 = 1892.
2) Subtract the result from the remaining part of the number: 194 – 1892 = 54.
3) Since 54 is not divisible by 973, 1946 is not divisible by 973.
Problem 2
Check the divisibility rule of 973 for 4865.
No, 4865 is not divisible by 973.
Explanation
To determine divisibility by 973:
1) Double the last three digits: 865 × 2 = 1730.
2) Subtract this from the rest of the number: 48 – 1730 = -1682.
3) Since -1682 is not a multiple of 973, 4865 is not divisible by 973.
Problem 3
Is -2919 divisible by 973?
Yes, -2919 is divisible by 973.
Explanation
For negative numbers, ignore the sign and check divisibility:
1) Double the last three digits: 919 × 2 = 1838.
2) Subtract from the remaining number: 29 – 1838 = -1809.
3) Since -1809 is not a multiple of 973, -2919 is not divisible by 973.
Problem 4
Can 3888 be divisible by 973 following the divisibility rule?
No, 3888 isn't divisible by 973.
Explanation
Check divisibility by 973 with these steps:
1) Double the last three digits: 888 × 2 = 1776.
2) Subtract from the rest of the number: 3 – 1776 = -1773.
3) Since -1773 is not a multiple of 973, 3888 is not divisible by 973.
Problem 5
Check the divisibility rule of 973 for 9730.
Yes, 9730 is divisible by 973.
Explanation
Follow the steps for checking divisibility by 973:
1) Double the last three digits: 730 × 2 = 1460.
2) Subtract from the remaining number: 9 – 1460 = -1451.
3) Since -1451 is not a multiple of 973, 9730 is not divisible by 973.
FAQs on Divisibility Rule of 973
1.What is the divisibility rule for 973?
2.How many numbers are there between 1 and 5000 that are divisible by 973?
3.Is 1946 divisible by 973?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 973 apply to all the integers?
Yes, the divisibility rule of 973 applies to all the integers.
- 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 973 if it follows the specific steps outlined for 973.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 973 are 973, 1946, 2919, etc.
- Integers: Integers are the 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: The process of ensuring the correctness of a result, such as using division to verify if a number is divisible by 973.
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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.
