If you happen to be viewing the article Introduction to Divisibility? on the website Math Hello Kitty, there are a couple of convenient ways for you to navigate through the content. You have the option to simply scroll down and leisurely read each section at your own pace. Alternatively, if you’re in a rush or looking for specific information, you can swiftly click on the table of contents provided. This will instantly direct you to the exact section that contains the information you need most urgently.
A divisibility rule is a shorthand and useful way of determining whether a given integer is divisible by a fixed divisor without performing the division, usually by examining its digits. Although divisibility tests exist for numbers in any radix or base, they are different. Imagine 3 friends trying to share 10 cookies. Each gets 3 cookies, and there’s one left over. They are unsure what to do with it; would one person get an extra cookie? That did not seem fair to the 3 friends, who loved sharing everything equally.
If there were 9 cookies, they would have divided the cookies equally, and there would have been no confusion. 9 is divisible by 3. This means that 9 cookies could have been divided into three equal parts without any extra cookies left. Further, we will study divisibility rules by applying their rules.
Divisibility Concept
Contents
Divisibility Rules
This section will teach about basic divisibility tests from 2 to 8. The divisibility rule of 1 is not required since every number is divisible by 1. Here are a few basic divisibility rules:
Divisibility Tests by 9 and 11
Divisibility test by 9: The sum of all the digits of the number should be divisible by 9.
Example: Using the divisibility rule of 9, state whether 724 is divisible by 9 or not.
Ans: Let us find the sum of all the digits of the number 724.
7+2+4 = 13
Here, 13 is not divisible by 9, so as per the divisibility test of 9, 724 is not divisible by 9.
Divisibility test by 11: The divisibility by 11 rule states that if the difference between the sum of the digits at odd places and the sum of the digits at even places of the number, is 0 or divisible by 11, then the given number is also divisible by 11.
Example: Test the divisibility of the 86416 by 11.
Ans: In 86416, if we take the alternate digits starting from the right, we get 6, 4, and 8 and the remaining alternate digits are 1 and 6. Now, 6 + 4 + 8 = 18, and 1 + 6 = 7. After finding the difference between these sums, we get 18 – 7 = 11, which is divisible by 11. Therefore 86416 is divisible by 11. It is to be noted that these alternate digits can also be considered as the digits on the odd places and the digits on the even places.
Divisibility Rule of 25
Divisibility by 25 means that a number is divisible by 25. A number is divisible by 25 if the last or the final two digits of the number are divisible by 25. For example, 125 is divisible by 25 because the last two digits, 25, are divisible by 25.
When a number is divisible by 25, it means that the number can be divided evenly by 25. The number 50 is divisible by 25 because it can be evenly divided into two groups of 25. 100 is divisible by 25 because it can be evenly divided into four groups of 25.
Example: Check whether 5200 is divisible by 25.
Ans: According to the divisible rule of 25, if the last two digits of a number are zeroes or the number formed by the last two digits is a multiple of 25, then the number is divisible by 25.
In the given number 5200, the last two digits are zeroes.
So, the number 5200 is divisible by 25.
Solved Examples
Q1. A number is divisible by 4 and 12. Check if it is divisible by 48.
Ans: 48 = 4 × 12 but 4 and 12 are not coprime.
No, it’s not necessary that the number will be divisible by 48.
Q2. Salma wants to distribute 123 toffee equally among 15 of her friends. Use the rules of divisibility and check whether she will be able to do so.
Ans: 123 toffees distributed to 15 friends
$=1+2+3=6 div 3=text { Yes }(6 text { is divisible by } 3)$
$=123 div 5=text { No }(123 text { is not divisible by } 5)$
No, she cannot distribute 123 toffee equally.
Q3 Without actual division, find if 235948 is divisible by 4.
Ans: The number formed by the last two digits on the extreme right side of 235948 is 48
48 ÷ 4 = 12, i.e. 48 is divisible by 4.
Therefore, 235948 is divisible by 4.
Practice Questions
Q1 Check whether 4410 is divisible by 45 or not.
Ans: Yes,4410 is divisible by 45.
Q2 State if the first number is divisible by the second number.
51 by 6
Ans: No, 51 is not divisible by 6.
Q3 Is 153 divisible by 9?
Ans: Yes
Summary
Divisibility rules in math are a set of specific rules that apply to a number to check whether the given number is divisible by a particular number or not. In this article, we have seen the divisibility rules for different numbers. The divisibility rule of 9 says that the sum of the digits of the given number should be divisible by 9. However, the divisibility rule of 11 states that a number is divisible by 11 if the difference between the sum of the digits at even places and odd places is 0 or divisible by 11. Later on, we learned about the divisibility rule of 25. i.e. If the last or the final two digits of a number are divisible by 25, then the whole number is divisible by 25. In the end, we added some solved examples and practice problems to check the divisibility rules.
Thank you so much for taking the time to read the article titled Introduction to Divisibility written by Math Hello Kitty. Your support means a lot to us! We are glad that you found this article useful. If you have any feedback or thoughts, we would love to hear from you. Don’t forget to leave a comment and review on our website to help introduce it to others. Once again, we sincerely appreciate your support and thank you for being a valued reader!
Source: Math Hello Kitty
Categories: Math
