definition divisibility rules 2 3 4 5 6 7 8 9 10
Answers
Step-by-step explanation:
Divisibility by 1
Every 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 rules for 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 rules for 7
Remove the last digit of the number and double it. Subtract from remaining number. The number should be 0 or two digit multiple of 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 x 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.
Answer: By looking at the digits of an integer, a divisibility rule can be used to quickly and conveniently determine if it can be divided by a specific number.
Step-by-step explanation:
Divisibility by 1: Each integer can be divided by 1. The 1 cannot be divided, and there is no special restriction. No matter how big the number is, dividing it by 1 yields the number itself. For instance, the number 3 is entirely divisible by 1, as is the number 3000.
Divisibility by 2: Any even number or number with an even last digit, such as 2,4,6,8, or 0, is always entirely divisible by 2. For instance, 509 is not divisible by 2 because it is not an even number, whereas 508 is an even number and is divisible by 2. The steps to determine whether or not 508 is divisible by two are as follows: Think about the number 508. Simply divide the final digit, 8, by 2. The number 508 is also divisible by two if the last digit, 8, is likewise divisible by two.
Divisibility rules for 3: According to this rule, 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. Think about the number 308. Take the sum of the digits (3+0+8=11) to see if 308 is divisible by 3 or not. Now determine whether or not the sum is divisible by 3. The initial number must also be divisible by three if the sum is a multiple of three. In this case, 308 is likewise not divisible by 3 because 11 is not divisible by 3. Similarly, 516 is entirely divisible by 3 because the total of its digits, 5+1+6, is 12, which is a multiple of 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. Consider the number 2308. Take a look at the last two digits. Since the number 8 is divisible by 4, so is the initial number 2308.
Divisibility by 5: All numbers that end in 0 or 5 are divisible by 5.
An illustration would be 10, 10000, 10000005, 595, 396524850, etc.
Divisibility by 6: The number 6 can be divided by any number that can be divided by both 2 and 3. In other words, if the given number's last digit is even and its digits added together are a multiple of 3, then it is also a multiple of 6. Example: Since the last digit of the number 630 is 0, it can be divided by two. Numbers 6+3+0 add up to 9, which is also divisible by 3. 630 can be divided by 6 thus.
Divisibility rules for 7 : Take the number's last digit out, then multiply it by two. Subtract the remainder from the total. The number must be a two-digit multiple of seven or zero. Is 1073 divisible by 7 as an example? Remove three from the number according to the rule, then double it to get six. 107 is now the remaining number, therefore 107-6 equals 101. If we go through the process once more, we get 1 x 2 = 2. The remainder, 10, minus 2, equals 8. The number 1073 cannot be divided by 7 since 8 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. Take the number 24344, for instance. Think about the last two numbers, which are 344. The original number 24344 is likewise divisible by 8, just as 344 .
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.
Consider the number 78532. Since the sum of its digits is 25, which cannot be divided by 9, 78532 cannot be divided by 9.
Divisibility by 10: Any number whose last digit is zero is divisible by 10 according to the rule of divisibility for the number 10. For instance: 10, 20, 30, 1000, 5000, 60000, etc.
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