Prime Factors, Perfect Squares, Oh My!

eX.A.K.R. SG

Sorry if I'm seem to be spamming up this forum, but I have been stumped by yet another question, which goes like this:

(a) Express 525 as the product of prime factors

I worked out the answer as:

525 = 3 x 5^2 x 7

Using the number triangle method:

525

| \

3 175

| | \

3 5 35

| | | \

3 5 5 7

(b) Given that the LCM of 15, x, and 35 is 525, find the two possible values of x between 15 and 35.

I worked out the answers of 25 and 21, using this method:

3 x 5 = 15; 5 x 5 = 25; 3 x 7 = 21; 5 x 7 = 35

Is this the right method?

But what is stumping me is this one:

The answer given is 21. How do I find it?

Ahm97sic SG

Hi eX.A.K.R.,

Use prime factorisation or number traingle method first for 525 and we will get 525 = 5 x 5 x 21, next

525k = 5^2 x 21 x k

To make 525k as a perfect square, k must be 21 so that 21 x k = 21 x 21 = 21^2.

This topic is very common in recent years "O" level E. Maths exam.

Regards,

ahm97sic

Maith SG

c) i always do trial and error :D iuse calculator type 525 x 1 =525 then square it see got a integer or not. If dont have,i try 525 x 2 =1050 then square it see got integer. I keep trying until i get a integer! lol

^tamago^ SG

square root u mean? Surprised

Lee012lee SG

Oh my god, trial and error, primary school uses trial and error, "O" level also uses trial and error, so JC, poly and university also use trial and error ???

eagle SG

this is to make it clearer

525 = 3 x 5² x 7

Obviously, it is not a square.

So, for 525k to be a square,
to find the smallest number k,
525k = 3² x 5² x 7² ======> This is a perfect square
3 x 5² x 7 x k = 3² x 5² x 7²

So, k = 3 x 7 = 21

eX.A.K.R. SG

I see... thanks for the help, Ahm97sic and eagle.

eX.A.K.R. SG

Trial and error could take too long... can you imagine the amount of time it could take to reach the answer in your method? What if the answer was some large integer like 100?

gunner77 SG

i only know how to do (C)

tis is wat my teacher taught me.

525k = perfect sq

(3 x 5^2 x 7) k = perfect sq

as u can see, only the number 5 has sq.

so make the 3 and 7 sq too then u will get the answer.

so the answer is 7x3 = 21

i know my explaination sucks. sorry

gunner77 SG

and ya just to add on,

they might not ask u only based on perfect sq

they might also ask u on perfect cube (^3)

Huatho SG

For first part, x = 25 (only one value).

Because, LCM of 15, 21, 35 is 105.