144 LearnersLast updated on May 26th, 2025
Divisibility Rule of 59
The divisibility rule is a way to determine 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 59.
What is the Divisibility Rule of 59?
The divisibility rule for 59 is a method by which we can find out if a number is divisible by 59 or not without using the division method. Check whether 1180 is divisible by 59 with the divisibility rule.
Step 1: Multiply the last digit of the number by 5, here in 1180, 0 is the last digit. Multiply it by 5. 0 × 5 = 0
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 118–0 = 118.
Step 3: As it is shown that 118 is not a multiple of 59, repeat the process:
Repeat Step 1 with the new number: Multiply the last digit of 118 by 5. 8 × 5 = 40
Subtract from the remaining digits: 11–40 = -29.
Step 4: Consider the absolute value for divisibility check. As 29 (absolute value of -29) is not a multiple of 59, the number 1180 is not divisible by 59.
If the result from the subtraction is a multiple of 59, then the original number is divisible by 59.
Tips and Tricks for Divisibility Rule of 59
Learning the divisibility rule can help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 59.
Know the multiples of 59:
Memorize the multiples of 59 (59, 118, 177, 236, 295… etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 59, then the number is divisible by 59.
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 59.
For example: Check if 3541 is divisible by 59 using the divisibility test. Multiply the last digit by 5, i.e., 1 × 5 = 5. Subtract from the remaining digits, 354–5 = 349.
Since 349 is a large number, repeat the process:
Multiply the last digit by 5, 9 × 5 = 45.
Subtract from the remaining digits, 34–45 = -11.
Since 11 is not a multiple of 59, 3541 is not divisible by 59.
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 59
The divisibility rule of 59 helps us quickly check if a given number is divisible by 59, but common mistakes like calculation errors lead to incorrect calculations. Here we will understand some common mistakes that will help you avoid them.
Mistake 1
Not following the correct steps. Solution
Students should follow the correct steps, such as multiplying the last digit by 5 and then subtracting the result from the remaining digits, excluding the last digit, and checking whether it is a multiple of 59.
Divisibility Rule of 59 Examples
Problem 1
Is 2360 divisible by 59?
No, 2360 is not divisible by 59.
Explanation
To determine if 2360 is divisible by 59, follow the steps below:
1) Take the last digit of the number, which is 0, and multiply it by 5, resulting in 0 × 5 = 0.
2) Subtract this result from the remaining leading number: 236 - 0 = 236.
3) Check if 236 is divisible by 59. Since 236 ÷ 59 is not an integer, 2360 is not divisible by 59.
Problem 2
Check the divisibility rule of 59 for 826.
No, 826 is not divisible by 59.
Explanation
For checking the divisibility of 826 by 59, follow these steps:
1) Multiply the last digit, 6, by 5, giving 6 × 5 = 30.
2) Subtract this product from the rest of the number: 82 - 30 = 52.
3) Check if 52 is divisible by 59. Since 52 is less than 59 and not a multiple, 826 is not divisible by 59.
Problem 3
Is -2950 divisible by 59?
Yes, -2950 is divisible by 59.
Explanation
To determine divisibility for -2950, we first remove the negative sign and follow the rule:
1) Multiply the last digit, 0, by 5, resulting in 0 × 5 = 0.
2) Subtract this from the rest of the number: 295 - 0 = 295.
3) Check if 295 is divisible by 59. Since 295 ÷ 59 equals 5, -2950 is divisible by 59.
Problem 4
Can 3541 be divisible by 59 following the divisibility rule?
No, 3541 isn't divisible by 59.
Explanation
To verify divisibility for 3541, perform the following:
1) Multiply the last digit, 1, by 5, resulting in 1 × 5 = 5.
2) Subtract this from the remaining number: 354 - 5 = 349.
3) Check if 349 is divisible by 59. Since 349 ÷ 59 is not an integer, 3541 is not divisible by 59.
Problem 5
Check the divisibility rule of 59 for 1180.
Yes, 1180 is divisible by 59.
Explanation
To check divisibility of 1180 by 59, follow these steps:
1) Multiply the last digit, 0, by 5, giving 0 × 5 = 0.
2) Subtract this product from the remaining number: 118 - 0 = 118.
3) Check if 118 is divisible by 59. Since 118 ÷ 59 equals 2, 1180 is divisible by 59.
FAQs on Divisibility Rule of 59
1.What is the divisibility rule for 59?
2.How many numbers are there between 1 and 300 that are divisible by 59?
3.Is 118 divisible by 59?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 59 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 59?
7.What are some fun ways kids in United States can practice Divisibility Rule of 59 with numbers?
8.What role do numbers and Divisibility Rule of 59 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Divisibility Rule of 59 skills?
Important Glossaries for Divisibility Rule of 59
- 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 even numbers.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example: multiples of 59 are 59, 118, 177, 236, 295, etc.
- 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.
- Absolute value: The absolute value of a number is its distance from zero on the number line, without considering its sign. For example, the absolute value of -11 is 11.
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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.
