Divisibility is an essential part of mathematics.
Consider a group of three people attempting to divide up ten cookies. There are three cookies for everyone and one cookie left over. No one knows what to do with it; would one person get an additional cookie, for example? The three buddies, who always shared everything, felt that was unfair.
It would have been clear who got how many cookies if there had been nine. For the simple reason that 9 may be divided into 3 parts. This indicates that there would have been no leftover cookies after dividing the 9 cookies into thirds.
Meaning of the Word Divisible
If there is no residue when dividing a number by another number, then the two numbers are said to be precisely divisible.
Standards for Dividing
The divisibility rules refer to a collection of guidelines for determining whether or not a given integer is truly divisible by another.
If you want to know if a given number is completely divisible by another, you can use divisibility rules as a quick check.
Let’s have a look at some rules for dividing:
Divisibility Rule for 1
One may always divide any number by 1.
Consider any number, large or small, from 423 to 45678, and you’ll see they’re all divisible by 1.
Divisibility Rule for 2
The sum of any two even numbers equals 4. When you divide by 2, any integer that ends in 2, 4, 6, 8, or 0 leaves you with zero. To give just a few examples, the numbers 12, 46, and 780 are all divisible by 2.
Divisibility Rule for 3
A number is said to be divisible by three if and only if the sum of its digits is divisible by three. Consider figure 753.
- Because 15 can be divided into thirds, so can 753.
Divisibility Rule for 4
The entire integer is divisible by 4 if and only if the sum of the number’s last two digits is divisible by 4.
Consider the number 3224 as an illustration.
A number divisible by 4 can be formed by adding the last two digits, which in this case are 24. This means that 3224 can be divided by 4 as well.
Divisibility Rule for 5
A number is evenly divisible by 5 if and only if it ends in 0 or 5. The numbers 35, 790, and 55 are all divisible by 5.
Divisibility Rule for 6
A number is also divisible by 6 if it can be divided by 2 and 3. For instance, since 12 can be divided by both 2 and 3, it may also be divided by 6.
Divisibility Rule for 7
There is some complexity to this meaning.
It follows that a number is evenly divisible by 7 if the difference between the double of the final digit and the remaining digits is divisible by 7.
Is that clear? Take the number 343 as an experiment.
The sum is 3, so that’s the final digit.
Six is twice as large as three.
The remainder after subtracting 6 from each of the remaining numbers, gives us, which is evenly divisible by 7.
Therefore, 343 can be divided by 7 as well.
Divisibility Rule for 8
Like the previous one, this one requires some practice to really grasp.
An integer is divisible by 8 if the sum of its last three digits is divisible by 8.
So, the last three digits of the number 4176 add up to 176.
Calculated by slicing 176 into eighths, we get:
Divisibility Rule for 9
The rule of 9 divisibility is very similar to the rule of 3 divisibility in that if the sum of the digits of a number is divisible by 9, then the number itself is divisible by 9.
Say the number 882 is an illustration.
Divisibility Rule for 10
An integer is divisible by 10 if and only if its final digit is 0.
Examples of divisible by 10 numbers include 200, 30, and 67890.
Divisibility Rule for 11
This rule of divisibility stands out as one of the most intriguing.
A number is divisible by 11 if and only if the difference between the sums of its odd and even digits is zero or a number is divisible by 11.