Help with this Prime factor sq root example

silverpuma · 2014-03-05 07:54:38

Hi all, I need some hand holding. I just finished the GCSE foundation text book all 600 pages and after doing 3 full previous exams under exam conditions, timed etc I managed an average of 97% so I have a reasonably good grasp of the basics.

I just started the higher text book and just on page 16 after some pages on powers, roots primes, factors, multiples and then HCF and LCF (using prime factors) I arrived at examples 24 and 25 (see image of actual textbook page) it seemed to just jump up a level in understanding and I do not understand what the end of example 23 means: "Therefore 21 is the smallest value which 55125 can be multiplied by to give a cube number"

http://1drv.ms/1jS59Ud [url added]

I understood all that came before this but I'm confused as to how this relates or builds upon what I have already learned......probably my 1.5 brain cells overheating....:-) Where on the MIF site could I get some info that would help me understand this question and example 24 and especially 25 better. I want to know why this works etc....... thanks and sorry for not being the sharpest chisel in the box!!!

bobbym · 2014-03-05 08:15:36

Hi;

It has to do with adding exponents when you multiply numbers with them.

They have factored 55125 as

Because 7^2 * 7 ( which is really 7^1 ) = 7^3

so if you multiply

now just the 3^2 remains, it too must be turned into a cube. We know that 3^2 x 3 ( which is really 3^1 ) = 3^3

To recap, we multiplied by a 7 and then by a 3. 7 x 3 = 21.

Try here and let me know how you are doing.

http://www.mathsisfun.com/exponent.html

Follow the links. Do not worry about what you do not get immediately. Read it and skip over it if necessary. Try to absorb what you can at your own pace. Good luck and congratulations on what you have achieved so far. See you later, bedtime.

silverpuma · 2014-03-05 09:25:32

thanks bobbym, things are becoming clearer. I'll feast on the MIF page after supper.....yum yum.

This is completely unrelated to my question but I'm curious, my son can do his UK GCSE higher maths exam at the end of year 11 and then additional maths (the cces board is changing the name this year to Further maths) at the end of year 12 so if all goes well he will have 2 GCSE maths and then begin 2 years of A-Level maths. The additional/further qualification is like a bridge between GCSE and A-Level and is via the ccea exam board. Does the English set-up have an equivalent "in between" type qualification.

FYI the additional/further qualification contain

Course Content

The course is divided into two sections, namely Pure Mathematics and Mechanics and Statistics. Topics covered in each section are detailed below.

Pure Mathematics    Mechanics and Statistics
Algebra    Linear Motion
Matrices    Summarising Data
Trigonometry    Newton's Law
Logarithms    Time Series
Differentiation    Equilibrium and Motion
Integration    Bivariate Analysis
   Moments of Forces
   Probability

Does edexcel or aqa etc have similar?

bobbym · 2014-03-05 16:48:26

Hi silverpuma;

The only thing I know about your country is "Rumpole of the Bailey." and Stonehenge. You will have to wait until Bob is here for that.

Bob · 2014-03-05 20:21:05

hi silverpuma,

I thought you were British based. I see that ccea is Northern Island.

I've been out of School for 4 years now so my knowledge of which exams are available is rusty.

Here are the exam board home pages. You will find a huge list of qualifications. Exam syllabuses have been in a state of flux for years; ever since the government of the day thought that showing an interest in education is a vote winner. The current secretary of State for Education lurches about throwing fresh ideas into the ring every few weeks. He wants to turn the clock back to the good old days of O levels (after all look what it did for him ) and at the same time keeps looking abroad to try and pinch the best of what's available elsewhere. GCSEs and A levels are about to be revised again; you'll find all the boards have advice about this, but the usual pattern is they have to rush about like headless chickens trying to work out what the latest reforms actually mean. There is no exam that is independent of this interference. (Sorry to show my bias here ... I remember the days when schools and boards just got on with it, without hassle. )

http://www.edexcel.com/Pages/Home.aspx

http://www.aqa.org.uk/

http://www.ocr.org.uk/

I had a search myself and the only syllabus that I found like the one you've described is this:

http://www.edexcel.com/quals/igcse/igcs … fault.aspx

but it's possible the others have them too, and I've just missed it.

Did you mean GCSE then 1 year extra GCSE then 2 more years A level ? What's to stop doing the extra concurrently with year 1 A level to short cut the process?

Bob

silverpuma · 2014-03-06 03:59:54

Thanks guys for the help and after my MIF reading last night and a period of head scratching my maths question became crystal clear and I'm happy to move on to the next page on my text book. I really enjoy this when something is fuzzy and then all of a sudden it begins to make sense.

@bob bundy The way my son's school works is that the students study Key stage 3 over yr 8-10. Then the majority of the year will do their maths higher GCSE over 2 years (y11 - y12). But some who show the ability and interest (so far my son is in this group) do this GCSE higher maths in 1 year instead of 2 , at the end of y11. Then they do this additional/further maths exam at the end of y12 so they have 2 maths qualifications during this 2 year period, where most have the normal 1 GCSE maths qualification over 2 years. Then they begin the normal A-Level course over 2 years. For this the school uses the edexcel A-Level course C1 C2, C2, C4 M1 and S1.

Bob you said above...

"Did you mean GCSE then 1 year extra GCSE then 2 more years A level ? What's to stop doing the extra concurrently with year 1 A level to short cut the process?"

I think the main thing is that since this additional/further 1 year maths qualification over 1 year is a bridge to A-Levels and include subjects that are in the first year A-Level so there would be too much overlap and double learning at the same time. But that's just me thinking out loud.

Another question just popped into my mind:-) When finding the prime factors of large number without a calculator I noticed that sometimes I would be unsure if a 3 or a 7 or a 11 for example would divide equally. I know a even number will divide by 2 and 5 divide into numbers ending with 0 and 5 but is their shortcut ways to find if a 3,7,11,13 etc will divide other than doing the full division? ....I appreciate all the help

bobbym · 2014-03-06 04:04:39

For 3, add the digits of the number. If the digit sum is divisible by 3 then so is the number.

Example: Is 1234567854 divisible by 3?

1+2+3+4+5+6+7+8+5+4 = 45. 45 is divisible by 3 so 1234567854 is divisible by 3.

Take a look here:

http://www.mathsisfun.com/divisibility-rules.html

Math Is Fun Forum

#1 2014-03-05 07:54:38

Help with this Prime factor sq root example

#2 2014-03-05 08:15:36

Re: Help with this Prime factor sq root example

#3 2014-03-05 09:25:32

Re: Help with this Prime factor sq root example

#4 2014-03-05 16:48:26

Re: Help with this Prime factor sq root example

#5 2014-03-05 20:21:05

Re: Help with this Prime factor sq root example

#6 2014-03-06 03:59:54

Re: Help with this Prime factor sq root example

#7 2014-03-06 04:04:39

Re: Help with this Prime factor sq root example

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