The best method to solve this question is by taking the number (24) and dividing it by the first prime number you can think of. We are lucky that 24 is even since that means we can divide it by 2. 

24/2 = 12

Then we take the number 12 and, again divide it by any prime number. In this case this could be 2 or 3 but for simplicity, let's choose 2.

12/2 = 6

The only prime number that 6 is divisible by is 3

6/3 = 2 

We can see that we have now reached a solution (the number 2) which is a prime number. To then factorise it we take the prime number results we got (aka 2) and multiply it by all the other prime numbers we divided the original number by (aka 3, 2 and 2)

Therefore 24 = 2 x 2 x 2 x 3

Hope you can solve other questions now!

Hey!
 2 × 2 × 2 × 3=24
4 times 6 =24
Hope this helps.

Secondary

Maths

Express 24 as a product of its prime factors?

For this question you must remember BODMAS (the order of signs):

Brackets
Order
Division
Multiplication
Addition
Subtraction

3 to the power of 3 belongs to "Order" and therefore comes before multiplication and division. So, we have to calculate all the numbers to the power of another first. I have notated 3 to the power of 3 as 3^3 below.

3^3=27
3^4=81
3^2=9

Now, although division comes before multiplication in BODMAS, it doesn't really matter which order you do them in. I usually just go from the left to the right which gives us:

3^3 x 3^4 / 3^2 =
27 x 81 / 9 = 243

So your answer is 243

Hope this helps!

A-Level

3 to the power of 3 ×3 to the power of 4 ÷ 3 to the power of 2?

There are 2 ways we could solve this question.

THE LONG WAY:

We add 3% to the capital sum (i.e. 2000 pounds) to find how much money we have after 1 year and then add 3% percent to that sum to find how much you have after two years. 

If the compound interest is 3% then that essentially means that after 1 year you have 103% of the original i.e. we have 100% of the original which is just the value of the original, plus 3% of the original so 103% in total. If we convert 103% into a decimal by dividing it by 100 we get 1.03. So, to find how much 103% of the capital sum (2000 pounds) is, we have to multiply it by 1.03:

2000 x 1.03 = 2060

So we have 2060 pounds after 1 year. In the second year, further 3 percent are added to the amount we have after 1 year. It is *compound* interest so this means after 2 years we have 103% of 2060 pounds and not 106% of 2000 pounds. To find 103% of 2060 pounds we do:

2060 x 1.03 = 2121.80 pounds

This is how much we have in our account after two years.

But, we can also do this 
THE SHORT WAY:

Using the formula C*((1+r)^t) where
r = interest rate
t = the number of years

To simplify: 1+r is exactly what we established above: 1.03. It shows what percentage of the original we have after one year expressed in decimal form. So in this case 103% or 1.03.

We then raise this value to the number of years so 1.03 to the power of 2 

1.03^2 = 1.0609

This number is then multiplied by the capital sum, 2000 pounds:

2000 x 1.0609 = 2121.80 pounds

This is the same answer as using the long way.

Hope this helps!

If £2000 is placed into a bank account that pays 3% compound intrest per year, how much will be in the account after 2 years?

Hi, I have broken down the steps below:

1. First we want to get all the digits without x or y on one side. In this case it's best to put them all on the left side where 2y is since it means we have less work  later. To do so we add 18 to both sides (the opposite of -18), so:

2y + 3 + 18 = 5x - 18 +18
2y + 21 = 5x

2. Now we want to get rid of the coefficient of x (the number in front of x). To do so we have to do the opposite operation. In this case x is being multiplied by 5 so the opposite operation is dividing by 5:

(2y + 21) / 5 = 5x/5

We can leave the left hand side as a fraction or divide both terms by 5 so:

2/5 y + 21/5 = x

This is it rearranged.

Hope this helps!

Primary

Make x the subject of 2y+3=5x-18?

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Make x the subject of 2y+3=5x-18

If £2000 is placed into a bank account that pays 3% compound intrest per year, how much will be in the account after 2 years

3 to the power of 3 ×3 to the power of 4 ÷ 3 to the power of 2

Express 24 as a product of its prime factors

This is a "Redeanalyse" of the "Sportpalastrede" by Joseph Goebbels. It can be used by native German speakers as a guide as to how to structure and write a text analysis and by non-native German speakers as a reading practice. Have fun!

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IGCSE German First Language - Redeanalyse

This is a model answer to the 2012 BMAT Section 3 Essay Question:

"The scientist is not someone who gives the right answers but one who asks the right questions.
Explain what this statement means. Argue to the contrary that the right answers are more important than the right questions. To what extent do you agree that the right questions must be asked before science can progress?"

It scored 4.5A

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BMAT Section 3 Model Essay

An exemplary internal assessment aligned with the IB Chemistry requirements on the topic of whether the chain length of primary alcohols affects the enthalpy of combustion. This can be used as reference for the structure and necessary components of a Chemistry IA.

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IB Chemistry Internal Assessment

This is a practice coursework for IGCSE History with the question "Assess the significance of Helmut Kohl's 10-point program between the years 1982 and 1998". It scored 40/40. Even if this topic may not be relevant to your coursework question it may be helpful to use as a reference on how to structure an IGCSE History Coursework.

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