Answer:
To determine if a number is divisible by a certain number, we can apply the basic knowledge about divisibility rules of a number. To define DIVISIBILITY, it refers to the allowability of a number to be divided by a certain number without leaving any remainder. Knowing the divisibility rules will minimize the time spent when put into a particular situation where it can be applicable. Here are the divisibility rules of 3, 6 and 9.
The divisibility rule of 3 states that a number can be divided by 3 without leaving a remainder when the sum of all the digits of the numbers is also divisible by 3.
Let us say we need to determine if the number 1,569 is divisible by 3. So, let us just add all of its digits together.
1 + 5 + 6 + 9 = 21
Since the sum of all the digits is 21 which is divisible by 3, hence, the number 1,569 is divisible by 3.
The divisibility rule of 6 states that a number can be divided by 6 without leaving a reminder when the number is both divisible by 2 and 3. The divisibility of 3 is already stated above. For the divisibility of 2, it states that the number will only be divisible by 2 if the number is an even number which means it ends in 0, 2, 4, 6 or 8.
Let us take 2,316 as an example. It already ends in 6 so it is an even number. This means that it is already divisible by 2. Next, let us test this number if it is divisible by 3. Adding its numbers: 2 + 3 + 1 + 6 = 12. 12 is a number divisible by 3. Hence, 2,316 is divisible by 6.
The divisibility rule of 9 states that a number can be divided by 9 without any remainder when the sum of all the digits is divisible by 9.
Let us take 3,078 as an example. We just add the digits: 3 + 0 + 7 + 8 = 18. Since the sum 18 is divisible by 9, therefore, 3,078 is divisible by 9.
