How Do You Know if It Is Divisible by 3?

How to Tell if a Number is Divisible by 3

To examination if a number is divisible by 3, follow these steps:

1. Add together the private digits of the number to make a total.
2. If this total is divisible by 3, the original number is divisible past 3.
3. If you are non certain if the total is divisible by three, apply the first two steps to that number.

If a number is divisible by 3, it means that the number is in the 3 times table. A number that is divisible past three is a multiple of 3. The number can be divided exactly by 3 to leave no remainder.

In this example, we will utilize the divisibility past iii rule to test 5502. Is 5502 in the 3 times table?

A number is divisible by iii if the sum of its digits is likewise divisible by 3. For example, 5502 is divisible by 3 because 5 + 5 + 0 + 2 = 12. 12 is divisible by 3 and and so, 5502 is divisible by 3.

The first stride is to add together the digits of the number.

v + 5 + 0 + 2 = 12.

The next step is to check if this new, smaller number is divisible by 3.

12 is 4 × 3. 12 is in the three times tabular array and so, 5502 is as well in the three times table.

Nosotros can also cheque that each number in the working out is a multiple of 3 past adding its digits.

12 is a multiple of 3 considering i + two = iii.

Here is another instance of using the dominion for divisibility past 3 to test if a number is a multiple of three.

Is the number 409 a multiple of 3?

The showtime pace is to add the digits of the number.

4 + 0 + 9 = xiii.

The next pace is to decide if the sum of the digits is a multiple of 3.

13 is not a multiple of iii. It is not in the 3 times table. We can also run across that i + 3 = 4 and 4 is not a multiple of three, therefore thirteen is not a multiple of three.

thirteen is an case of a number that is non divisible by iii then, 409 is not divisible by 3.

A number is not divisible by 3 if the sum of its digits is not divisible by 3. 409 is not divisible by 3 considering 4 + 0 + 9 = 13 and thirteen 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 information technology not divisible by 3.

The rule for divisibility by 3 works for all numbers no affair how large.

For case, hither is the number 529, 943.

The starting time step is to add together the digits of the number.

5 + 2 + 9 + ix + 4 + 3 = 32

The side by side step is to test if the sum of the digits is divisible by 3.

32 is not divisible by three. Nosotros know this because 30 and 33 are multiples of 3 and 32 is in betwixt these numbers.

We can also use the same test on 32 to show that information technology is non divisible by 3. We add the digits. iii + 2 = 5 and 5 is not a multiple of 3.

32 is non a multiple of three and therefore 529, 943 is not a multiple of 3 either. 529, 943 is an instance of a number that is not divisible by 3.

Here is an example of testing a big number to see if it is in the iii times table.

Is 7, 749, 984 a multiple of iii?

Start past calculation the digits.

7 + 7 + 4 + ix + 9 + 8 + 4 = 48

48 is 16 × 3 and then, it is a multiple of 3.

If nosotros were not sure if the number was a multiple of 3, add the digits and see if the total is a multiple of iii.

iv + viii = 12, which is 4 × 3. 12 is a multiple of 3 and so, 48 is a multiple of 3 and 7, 749, 984 is also a multiple of 3

Why Does the Divisibility Rule for three Piece of work?

The divisibility rule for iii works because the number represented by each digit can be written as a multiple of 9 plus that digit. ix is divisible by three so if the sum of the digits is divisible past 3, the number itself is likewise.

Here is the proof that 3174 is divisible past three.

The digit 3 stands for 3000, which is 1000 × 3.

This is the same every bit 999 × three plus one more 3.

The digit 1 stands for 100, which is 100 × 1.

This is the same as 99 × i plus ane more ane.

The digit vii stands for seventy, which is 10 × 7.

This is the same as nine × vii plus ane more seven.

The digit 4 stands for one lot of iv.

The multiples of nine, 99 and 999 are all divisible by 3.

3174 is equal to 999 × 3 + 99 × 1 + 9 × vii plus three + 1 + seven + 4.

The multiples of ix, 99 and 999 are all divisible by 3, so we only need to cheque the sum of the digits: 3 + i + 7 + 4.

three + i + vii + 4 = 15, which is divisible by 3.

Since the multiples of 9, 99 and 999 along with the sum of the digits are all divisible by 3, the entire number is divisible by 3.

All numbers are written in base of operations x. This means that the digits of each number stand for a multiple of 9 plus that digit. The multiples of 9 are divisible by three, so we but need to examination the sum of the digits to see if the whole number is divisible by iii.

No matter what the number, add the digits to bank check if information technology is divisible past 3.

List of Numbers Divisible by 3

Hither is a list of 2-digit numbers less than 100 that are divisible by iii:

3, half-dozen, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96 and 99.

There are 33 two-digit numbers that are divisible past 3. The largest 2 digit number divisible by 3 is 99, which is 33 × 3.

This list tin help us to identify some mutual multiples of 3, which helps usa to identify if a larger number is divisible by 3.

Prime number numbers are non exist divisible past 3. This is because prime numbers can only be divided past 1 and themselves.

Even numbers tin can exist divisible by 3. For example, the even number of 12 is divisible by 3.

All numbers that are divisible by nine are besides divisible by iii. This is because three divides exactly into nine.

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Source: https://www.mathswithmum.com/rule-for-divisibility-by-3/