Write divisibility test of 2,3,4,5,6,9 and 11
Answers
Step-by-step explanation:
very number is divisible by 1. Divisibility rule for 1 doesn’t have any particular condition. Any number divided by 1 will give the number itself, irrespective of how large the number is. For example, 3 is divisible by 1 and 3000 is also divisible by 1 completely.
Divisibility by 2
Any even number or number whose last digit is an even number i.e. 2,4,6,8 including 0 is always completely divisible by 2.
Example: 508 is an even number and divisible by 2 but 509 is not an even number, hence not divisible by 2. Procedure to check whether 508 is divisible by 2 or not is as follow:
Consider the number 508
Just take the last digit 8 and divide it by 2
If the last digit 8 is divisible by 2 then the number 508 is also divisible by 2.
Divisibility by 3
Divisibility rule for 3 states that a number is completely divisible by 3 if the sum of its digits is divisible by 3 i.e., it is a multiple of 3
Consider a number, 308.To check whether 308 is divisible by 3 or not, take sum of the digits (i.e. 3+0+8= 11). Now check whether the sum is divisible by 3 or not. If the sum is a multiple of 3 then the original number is also divisible by 3. Here, since 11 is not divisible by 3, 308 is also not divisible by 3.
Similarly, 516 is divisible by 3 completely as the sum of its digits i.e. 5+1+6=12, is a multiple of 3.
Divisibility by 4
If the last two digits of a number are divisible by 4, then that number is a multiple of 4 and is divisible by 4 completely.
Example: Take the number 2308. Consider the last two digits i.e. 08. As 08 is divisible by 4, the original number 2308 is also divisible by 4.
Divisibility by 5
Numbers with last digit 0 or 5 are always divisible by 5.
Example: 10, 10000, 10000005, 595, 396524850 etc.
Divisibility by 6
Numbers which are divisible by both 2 and 3 are divisible by 6. That is, if last digit of the given number is even and the sum of its digits is a multiple of 3, then the given number is also a multiple of 6.
Example: 630, the number is divisible by 2 as the last digit is 0.
The sum of digits is 6+3+0 = 9, which is also divisible by 3.
Hence 630 is divisible by 6.
Divisibility by 7
The rule for divisibility by 7 is given below:
Divisibility rules for 7
Example: Is 1073 divisible by 7?
From the rule stated remove 3 from the number and double it, which becomes 6.
Remaining number becomes 107, so 107-6 = 101.
Repeating the process one more times, we have 1×2=2
Remaining number 10 – 2 = 8.
As 8 is not divisible by 7, hence the number 1073 is not divisible by 7.
Divisibility by 8
If the last three digits of a number are divisible by 8, then the number is completely divisible by 8.
Example: Take number 24344. Consider the last two digits i.e. 344. As 344 is divisible by 8, the original number 24344 is also divisible by 8.
Divisibility by 9
The rule for divisibility by 9 is similar to divisibility rule for 3. That is, if the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.
Example: Consider 78532, as the sum of its digits (7+8+5+3+2) is 25, which is not divisible by 9, hence 78532 is not divisible by 9
Divisibility by 10
Divisibility rule for 10 states that any number whose last digit is 0, is divisible by 10.
Example: 10, 20,30,1000,5000,60000 etc.
Divisibility by 11
If the difference of the sum of alternative digits of a number is divisible by 11 then that number is divisible by 11 completely.
In order to check whether a number like 2143 is divisible by 11 following is the procedure.
Group the alternative digits i.e. digits which are in odd places together and digits in even places together. Here 24 and 13 are two groups.
Take the sum of the digits of each group i.e. 2+4=6 and 1+3= 4
Now find the difference of the sums; 6-4=2
If the difference is divisible by 11, then the original number is also divisible by 11. Here 2 is the difference which is not divisible by 11.
Therefore, 2143 is not divisible by 11.
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Answer:
A divisibility rule is a convenient shorthand for checking if an integer is divisible by a given set divisor without actually doing the division, often by looking at the digits of the number.
Explanation:
Divisibility by 2
Any even integer or number with an even final digit, such as 2,4,6,8, or 0, is always entirely divisible by 2.
Example:
- 308 is an even number and divisible by 2 but 309 is not an even number, hence not divisible by 2.
- The steps to determine whether or not 308 is divisible by two are as follows:
- Think about the number 308
- Just take the last digit 8 and divide it by 2
- If the last digit 8 is divisible by 2 then the number 308 is also divisible by 2.
Divisibility by 3
A number is fully divisible by three if the total of its digits is also divisible by three, or if it is a multiple of three, according to the rule of three.
Example:
- Consider a number, 308.
- To check whether 308 is divisible by 3 or not, take some of the digits (i.e. 3+0+8= 11).
- Now determine whether or not the total is divisible by 3.
- The initial number must also be divisible by three if the total is a multiple of three.
- In this case, 308 is likewise not divisible by 3 since 11 is not divisible by 3.
Divisibility by 4
A number is a multiple of 4 and is fully divisible by 4 if its last two digits are also divisible by 4.
Example:
- Take the number 2308.
- Take a look at the last two numbers, or 08.
- Since the number 8 is divisible by 4, so too is the initial number 2308.
Divisibility by 5
All numbers that end in 0 or 5 may be divided by 5.
Example:
- The numbers which end with 0 are also divisible by 5 like 10, 10000, etc.
- The numbers which also end with 5 are also divisible like 105,1055 etc.
Divisibility by 6
- The number 6 may be divided by any number that can be divided by both 2 and 3.
- In other words, if the provided number's final digit is even and its digits added together are a multiple of 3, then it is also a multiple of 6.
Example:
- 630 has a final digit of 0, making it divisible by two.
- Numbers 6+3+0 add up to 9, which is also divisible by 3.
- Hence 630 is divisible by 6.
Divisibility by 7
The rule for divisibility by 7 is given below:
- Consider the number 1073 is it divisible by 7?
- Remove three from the number according to the rule, then double it to get six.
- 107 is now the last number, therefore 107-6 equals 101.
- Repeating the process one more time, we have 1×2=2
- Remaining number 10 – 2 = 8.
- As 8 is not divisible by 7, hence the number 1073 is not divisible by 7.
Divisibility by 8
A number is fully divisible by 8 if its last three digits are also divisible by 8.
Example:
- Consider the number 24344.
- Think about the final two numbers, 344.
- The original number 24344 is likewise divisible by 8, just as 344 is.
Divisibility by 9
The rule for division by nine is comparable to the method for division by three. In other words, a number is divisible by 9 if the sum of its digits is also divisible by 9.
Example:
- Take the number 78532 into consideration.
- Since the total of its digits is not divisible by 9 (25), which is 7+8+5+3+2, 78532 is not divisible by 9.
Divisibility by 10
The divisibility rule for 10 states that any number whose last digit is 0, is divisible by 10.
Example:
The numbers like 10, 20,30,1000,5000,60000, etc. which end with at least one zero are divisible by 10
Divisibility by 11
- A number is totally divisible by 11 if the difference between the sum of its alternate digits is divisible by 11.
- The process to determine if an integer, such as 2143, is divisible by 11 is as follows.
- The alternate digits, or those that are in odd or even locations, should be grouped together. These two groupings here are 24 and 13.
- Take the total of each group's digits, i.e., 2+4=6 and 1+3=4.
- Find the difference between the amounts now, 6-4=2.
- If the difference can be divided by 11, the original number can as well. Here, the difference is 2, which cannot be divided by 11.
- 2143 is therefore not divisible by 11.
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