Why are numbers divisible by 3

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Now live: A fully responsive profile. The unofficial elections nomination post. Linked Example 2: Using the rule of divisibility of 3, find out whether the given large number is divisible by 3 or not.

We know that 45 is divisible by 3 which means is also divisible by 3. Example 3: Using the rule of divisibility of 3, find out if the greatest 3-digit number is exactly divisible by 3 or not.

Solution: The greatest 3-digit number is The sum of all the digits of is divisible by 3 which means is also divisible by 3. A whole number is said to be divisible by 3 if the sum of all the digits of a whole number is exactly divided by 3; this rule is referred to as the divisibility rule of 3. Without doing division we can find out whether a number is divisible by 3 or not. Hence, 45 is said to be divisible by 3, because it gives the quotient as 15 and the remainder as 0. First, we need to check if the sum of all the digits of the given number is divisible by 3 or not.

We know that 3 is divisible by 3. Thus, is divisible by 3. According to the divisibility rule of 3, a number is said to be divisible by 3 if the sum of all digits of that number is divisible by 3.

For example, the number is exactly divisible by 3. If 55 is divided by 3 the quotient will come to 18 and the remainder will come to 1.

It is not in the 3 times table. A number is not divisible by 3 if the sum of its digits is not divisible by 3. Prime numbers are not divisible by 3 because they are ony divisible by 1 and themselves. For example, 13 is a prime number and so it not divisible by 3. For example, here is the number , We know this because 30 and 33 are multiples of 3 and 32 is in between these numbers.

We can also use the same test on 32 to show that it is not divisible by 3. We add the digits. Here is an example of testing a large number to see if it is in the 3 times table.

Is 7, , a multiple of 3? Start by adding the digits. If we were not sure if the number was a multiple of 3, add the digits and see if the total is a multiple of 3. The divisibility rule for 3 works because the number represented by each digit can be written as a multiple of 9 plus that digit. Here is the proof that is divisible by 3.

The digit 4 stands for one lot of 4. Tell me as quickly as possible! And luckily you have a little tool in your toolkit where you know how to test for divisibility by 3 Well, you say I can just add up the digits If the sum of that is a multiple of 3 then this whole thing is a multiple of 3 So you say 4 plus 7 plus 9 plus 2 That's Plus 9, it's Plus 2 is 22 That's not divisible by 3 If you're unsure, you can even add the digits of that 2 plus 2 is 4. Clearly not divisible by 3 So this thing right over here is not divisible by 3 And so luckily that emergency was saved But then you walk down the street a little bit more and someone comes up to you "Quick!

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