How do you decrease $£ 40$ by $15\% $?

Hint: Here first of all we will find the percentage of the given number. And then will subtract the value from the given number for the resultant required value.

Complete step-by-step solution:
First of all convert the given data in the form of mathematical expression.
$15\% $ of $£40$
Mathematical expression: $15\% \times £40$
It can calculate as: $ = \dfrac{{15 \times 40}}{{100}}$
Find the factors from the numerator and the denominator.
$ = \dfrac{{3 \times 5 \times 2 \times 2 \times 10}}{{10 \times 2 \times 5}}$
Common factors from the numerator and the denominator cancel each other. Therefore remove from the numerator and the denominator.
$ = 2 \times 3$
Simplify the above expression.
$ = 6£$
Now, subtract $£6$ from $£40$
Therefore, $£40 - £6$
Simplify the above expression:
 $£40 - £6 = £34$
This is the required solution.

Second Method:
Given that we have to decrease the given data by $15\% $ then the required will be rest of $15\% $
Therefore, it would be the same as $100\% - 15\% = 85\% $
Now, the required solution would be $85\% \;{\text{of £40}}$
It can be calculated as $ = \dfrac{{85 \times 40}}{{100}}$
Find the factors in the numerator and the denominator.
$ = \dfrac{{17 \times 5 \times 2 \times 2 \times 10}}{{10 \times 2 \times 5}}$
Common factors from the numerator and the denominator cancel each other. Therefore remove $10 \times 2 \times 5$ from the numerator and the denominator.
$ = 17 \times 2$
Simplify the above equation.
$ = £34$
This is the required solution.

Note: Be careful while finding the factors and simplification of the terms. You should be very good in multiples of the numbers. Prime factorization is the process of finding which prime numbers can be multiplied together to make the original number, where prime numbers are the numbers greater than $1$ and which are not the product of any two smaller natural numbers. Percentage is the fraction which is based upon the hundred.