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 Post subject: Factors and square numbersPosted: Sat Oct 29, 2011 9:51 am

Joined: Wed Sep 14, 2011 10:35 am
Posts: 75
I am stuck regarding a good method to approach the following questions (from past KS2 SATS papers apparently) apart from trial and error which is very time consuming. Is there a better way?

1. This four digit number is a square number. Write in the missing digits: 9 _ _ 9

2. The same number is missing from each box, write in the missing numbers:

_ x _ x _ = 1331

3. Write the three missing digits:

_ _ x _ = 371

Can you recommend a book/ revision guide which summarises this kind of thing? We have an old KS2 CGP guide but it doesn't really cover this. The test is in 3 weeks- do you think I will stress my DC covering this now (she can do "normal" factor/ multiple questions but these seem more challenging)?

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 Post subject: Re: Factors and square numbersPosted: Sat Oct 29, 2011 11:04 am

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 13992
Quote:
1. This four digit number is a square number. Write in the missing digits: 9 _ _ 9

100 x 100 is 10 000 so the number square is 90 something it would have to be 93 or 97 to get a 9 in the units and a quick estimate would eliminate 93, 97 squared is 9409

Quote:
2. The same number is missing from each box, write in the missing numbers:

_ x _ x _ = 1331

10 x 10 x 10 = 1000

so its going to be 11 (to get the one in the units digit)

Quote:
3. Write the three missing digits:

_ _ x _ = 371

Which digit could give us the 1 in the units - eliminate 2,4,6,8 also can't be 3 (or 9) as 371 digits don't add to a multiple of 3 and can't be 5 (all multiples end in 0 or 5) so what is left?

only 7

Then division gives 53 x 7 ...

Make up similar questions ... know square numbers

Last edited by Guest55 on Sat Oct 29, 2011 12:20 pm, edited 1 time in total.

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 Post subject: Re: Factors and square numbersPosted: Sat Oct 29, 2011 12:00 pm

Joined: Sun Jan 13, 2008 6:18 pm
Posts: 238
Location: Gloucestershire
10 x 10 x 10 = 100

I reckon this is 1000

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 Post subject: Re: Factors and square numbersPosted: Sat Oct 29, 2011 12:19 pm

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 13992
OK - just a typo - changed ...

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 Post subject: Re: Factors and square numbersPosted: Sun Oct 30, 2011 3:07 pm

Joined: Wed Sep 14, 2011 10:35 am
Posts: 75
Great, many thanks Guest55.

I didn't know that if the digits of a number added up to a multiple of 3, then that number would also be a multiple of 3.

Are there any other "short cuts" to finding factors of large numbers? (Apart from the fairly obvious ones I already know: any number ending in an odd digit will not be divisible by 2; any number ending in 0 or 5 will be divisble by 5).

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 Post subject: Re: Factors and square numbersPosted: Sun Oct 30, 2011 3:17 pm

Joined: Mon Jun 18, 2007 2:32 pm
Posts: 7137
Location: East Kent
1 everything!
2 even
3 digits add up to 3,6,9
4 even
5 end in 5 or 0
6 even
7..
8 even
9 digits add up to 9
10 ends in 0
11 11,22,33,44,etc
would love to find some others, I try to encourage pupils to go through the checklist for eliminating possibilities

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 Post subject: Re: Factors and square numbersPosted: Sun Oct 30, 2011 4:12 pm

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 13992
There is one for 7 but it's so complicated I don't bother remembering it .. from a website I quote:

Dividing by 4
Are the last two digits in your number divisible by 4?
If so, the number is too!
For example: 358912 ends in 12 which is divisible by 4, thus so is 358912.

Dividing by 6
If the Number is divisible by 2 and 3 it is divisible by 6 also.

Dividing by 7 (2 Tests)
Take the last digit in a number.
Double and subtract the last digit in your number from the rest of the digits.
Repeat the process for larger numbers.
Example: 357 (Double the 7 to get 14. Subtract 14 from 35 to get 21 which is divisible by 7 and we can now say that 357 is divisible by 7.
NEXT TEST
Take the number and multiply each digit beginning on the right hand side (ones) by 1, 3, 2, 6, 4, 5.
Repeat this sequence as necessary
If the sum is divisible by 7 - so is your number.
Example: Is 2016 divisible by 7?
6(1) + 1(3) + 0(2) + 2(6) = 21
21 is divisible by 7 and we can now say that 2016 is also divisible by 7.

Dividing by 8
This one's not as easy, if the last 3 digits are divisible by 8, so is the entire number.
Example: 6008 - The last 3 digits are divisible by 8, therefore, so is 6008.

Dividing by 9
Almost the same rule and dividing by 3. Add up all the digits in the number.
Find out what the sum is. If the sum is divisible by 9, so is the number.
For example: 43785 (4+3+7+8+5=27) 27 is divisible by 9, therefore 43785 is too!

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 Post subject: Re: Factors and square numbersPosted: Sun Oct 30, 2011 5:33 pm

Joined: Thu Jan 03, 2008 8:26 am
Posts: 1330
Location: Watford, Herts
The 7 rules sound no easier than just dividing, but this one is useful:

Dividing by 11
Add up every second digit, add up every other digit and if the difference is divisible by 11, so is the original number.
Example: 374: (3+4) - 7 = 0, so 374 is divisible by 11.
Example: 41723: (4+7+3) - (1+2) = 11, which is divisible by 11, so 41723 is too.

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 Post subject: Re: Factors and square numbersPosted: Sun Oct 30, 2011 6:07 pm

Joined: Mon Jun 18, 2007 2:32 pm
Posts: 7137
Location: East Kent
ta!

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 Post subject: Re: Factors and square numbersPosted: Mon Oct 31, 2011 6:25 pm

Joined: Wed Sep 14, 2011 10:35 am
Posts: 75
Fascinating! I don't ever remember learning this at school. Thanks yoyo, WP and Guest55.

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