167 LearnersLast updated on May 26th, 2025
Divisibility Rule of 159
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 159.
What is the Divisibility Rule of 159?
The divisibility rule for 159 is a method by which we can find out if a number is divisible by 159 or not without using the division method. Check whether 4773 is divisible by 159 with the divisibility rule.
Step 1: Multiply the last digit of the number by 9, here in 4773, 3 is the last digit, multiply it by 9. 3 × 9 = 27.
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 477–27 = 450.
Step 3: If the result from Step 2 is a multiple of 159, then the number is divisible by 159. If the result isn't a multiple of 159, then the number isn't divisible by 159. Since 450 is not a multiple of 159, 4773 is not divisible by 159.
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Tips and Tricks for Divisibility Rule of 159
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 159.
- Know the multiples of 159: Memorize the multiples of 159 (159, 318, 477...etc.) to quickly check for divisibility. If the result from the subtraction is a multiple of 159, then the number is divisible by 159.
- Use the negative numbers: If the result we get after the subtraction is negative, we will consider its absolute value 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 159.
For example: Check if 15918 is divisible by 159 using the divisibility test. Multiply the last digit by 9, i.e., 8 × 9 = 72.
Subtract this result from the remaining digits excluding the last digit, 1591–72 = 1519. Repeat the process: Multiply the last digit by 9, i.e., 9 × 9 = 81.
Now subtract 81 from the remaining numbers excluding the last digit, 151–81 = 70. Since 70 is not a multiple of 159, 15918 is not divisible by 159.
- 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 159
The divisibility rule of 159 helps us to quickly check if a given number is divisible by 159, but common mistakes like calculation errors can lead to incorrect conclusions. Here are some common mistakes and how to avoid them.
Mistake 1
Not following the correct steps.
Students should follow the correct steps, which are multiplying the last digit by 9 and then subtracting the result from the remaining digits excluding the last digit and checking whether it is a multiple of 159.
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 obtaining a large result from subtraction. The process should be repeated until we get the smallest number that is divisible by 159.
Mistake 4
Not considering the negative values.
Students disregard negative values thinking divisibility rules don't apply to negative values. But the divisibility rule is applicable for negative values too. So students should consider the absolute value while checking for divisibility.
Mistake 5
Confusing the steps
Students often confuse or forget the steps. To avoid these errors, students should practice regularly.
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Divisibility Rule of 159 Examples
Problem 1
Is the year 3180 divisible by 159?
Yes, 3180 is divisible by 159.
Explanation
To check divisibility by 159, we can use the following approach:
1) Multiply the last digit by 9, 0 × 9 = 0.
2) Subtract the result from the remaining digits, excluding the last digit, 318 - 0 = 318.
3) Repeat the process for 318: 8 × 9 = 72, 31 - 72 = -41.
4) Add the results of the second step to the absolute value of the third step, 318 + 41 = 359.
5) Check if 359 is divisible by 159. Since 359 is not divisible by 159, we need to continue the process until the result becomes zero or a known multiple of 159.
Problem 2
Check if the number 4773 is divisible by 159.
No, 4773 is not divisible by 159.
Explanation
To assess divisibility by 159:
1) Multiply the last digit by 9, 3 × 9 = 27.
2) Subtract this from the remaining digits, 477 - 27 = 450.
3) Check 450 for divisibility by 159 by repeating the process: 0 × 9 = 0, 45 - 0 = 45.
4) Since 45 is not a multiple of 159, 4773 is not divisible by 159.
Problem 3
Is -6369 divisible by 159?
Yes, -6369 is divisible by 159.
Explanation
Remove the negative sign and check divisibility for 6369:
1) Multiply the last digit by 9, 9 × 9 = 81.
2) Subtract the result from the remaining digits, 636 - 81 = 555.
3) Check 555: 5 × 9 = 45, 55 - 45 = 10.
4) Since 10 is not a multiple of 159, continue until you reach a known multiple or zero.
5) As it turns out, 6369 is divisible by 159 (159 × 40 = 6360).
Problem 4
Can 5005 be divisible by 159 following the divisibility rule?
No, 5005 is not divisible by 159.
Explanation
Check using the steps:
1) Multiply the last digit by 9, 5 × 9 = 45.
2) Subtract from the remaining digits, 500 - 45 = 455.
3) Check 455: 5 × 9 = 45, 45 - 45 = 0.
4) Since 0 is a multiple of 159, this means our calculations have shown an error in initial subtraction, but since 455 is not a multiple of 159, 5005 is not divisible by 159.
Problem 5
Verify if the number 7959 follows the divisibility rule of 159.
Yes, 7959 is divisible by 159.
Explanation
To verify:
1) Multiply the last digit by 9, 9 × 9 = 81.
2) Subtract from the remaining digits, 795 - 81 = 714.
3) Check 714: 4 × 9 = 36, 71 - 36 = 35.
4) Since 35 is not a multiple of 159, continue until you reach a known multiple or zero.
5) 714 itself is a known multiple of 159 (159 × 5 = 795).
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FAQs on Divisibility Rule of 159
1.What is the divisibility rule for 159?
2.How many numbers are there between 1 and 1000 that are divisible by 159?
3.Is 318 divisible by 159?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 159 apply to all integers?
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Important Glossaries for Divisibility Rule of 159
- 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 obtained after multiplying a number by an integer. For example, multiples of 159 are 159, 318, 477,...
- Integers: Integers are the numbers that include all whole numbers, negative numbers, and zero.
- Subtraction: Subtraction is a process of finding the difference between two numbers, by reducing one number from another.
- Absolute Value: The non-negative value of a number without regard to its sign. For example, the absolute value of -5 is 5.
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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.
