numeracy

[kathryrn 1]

what are the rules of dividing 3, 6, & 9?

[Buenchico]

If the sum of the digits is divisible by 3, the number is divisible by 3.

Example:
Consider 6447. The sum of the digits is 21 (which is divisible by 3), so 6447 is divisible by 3.

If the sum of the digits is divisible by 3 and the number is even, the number is divisible by 6.
So 6447 is not divisible by 6 but 6474 is.

If the sum of the digits of the sum of the digits is divisible by 3, the number is divisible by 9.
e.g. the sum of the digits of both 6447 and 6474 is 21. But the sum of the digits of 21 is 3. This is (obviously) divisible by 3, so both 6447 and 6474 are divisible by 9.

Chris

[kathryrn 1]

this question is for my 9 year old daughter for home work, can you explain it in an easier way please?

[Buenchico]

(2-part post):

I'll try again:

To see if a number can be divided by 3 (without a remainder, of course), first add up the digits, then see if the new number will divide by 3.

For example, if we want to know whether 789 can be divided by 3, we add up 7 + 8 + 9. That gives us 24. We know that 24 can be divided by 3 (because it's among the answers to the 3 times table), so 789 can also be divided by 3.

Let's try another one:
Can 671 be divided by 3? If we add up the digits, 6 + 7 + 1 comes to 14. That can't be divided by 3, so 671 can't be divided by 3.

Just one more:
Can 5439 be divided by 3? Adding up the digits gives us 5 + 4 + 3 + 9, which comes to 21. That can be divided by 3, so we know that 5439 can be divided by 3.

What about dividing by 6?
We can divide a number by 6 if it's even and the digits add up to a number which can be divided by 3.

So, can 5439 be divided by 6? Obviously not, because it's not an even number.

[Buenchico]

Can 6384 be divided by 6?
Well, it's even, so that's OK. Let's add up the digits: 6 + 3 + 8 + 4 = 21. 3 goes into 21, so 6384 passes both tests. Yes, it can be divided by 6.

What about dividing by 9?
To see if a number can be divided by 9, we add the digits up once - and then we add them up again! If 3 goes into the answer, 9 will go into the original number.

Here's an example:
Can 7102116 be divided by 9? If we add up all the digits, we get 18. Then we add up the digits in our answer: 1 + 8 = 9. Three goes into 9, so 9 will go into 7102116.

Lastly, let's take a massive number (over 2 billion!) and see whether it can be divided by 3, 6 and 9:
The number is 2,715,311,112
Adding up the digits comes to 24. That's in the answers to the 3 times table, so we know that our big number can be divided by 3.
But our big number is also even. So, it's passed both tests which tell us that it can be divided by 6.
What about dividing by 9? Well first we add up all the digits. We've just done that, the answer is 24. Then we add up the digits in our answer: 2 + 4 = 6. That's in the answers to the 3 times table, so yes, our big number can be divided by 9.

Chris

[Buenchico]

PS; If you want it worded as rules, try these:

3 will divide into a number if it will divide into the sum of the digits.

6 will divide into a number if 3 will divide into that number and the number is even.

9 will divide into a number if 3 will divide into the answer we get from summing the digits twice.

Chris

[Loosehead]

Chris, I pay homage to the master of patience! Respect!

[crokepark]

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23:36 Thu 26th Apr 2007