Question

If $d=HCF\left( 48,72 \right)$ find the value of d.

Answer 1

Hint: We solve this question by using the concept of prime factors. We represent each of the given numbers as a product of prime numbers. Then we take the Highest Common Factor or HCF of the given terms by considering the common factors for both the terms. This represents the value of d which is our required solution.

Complete step by step answer:
In order to solve this question, let us explain the concept of HCF or Highest Common Factor for any two numbers. Highest Common Factor of two numbers is the largest number which can divide both the numbers. For example, let us consider two numbers 9 and 15. They can be written in terms of prime factors given by $9=3\times 3$ and $15=3\times 5.$ Here, we need to take the largest common factor for both the numbers such that it completely divides them. In this case, the HCF is found to be 3.
For the given question, we are given as equation as,
$\Rightarrow d=HCF\left( 48,72 \right)$
d is obtained as a result of applying the HCF function to the two numbers 48 and 72. In order to find their HCF, we represent them in terms of the product of prime factors.
$\Rightarrow 48=2\times 2\times 2\times 2\times 3$
$\Rightarrow 72=2\times 2\times 2\times 3\times 3$
Now, we need to take the common factors whose product will give us the HCF. In this case, we can see that the common factors are 2, 2, 2 and 3. Taking the product of these prime factors,
$\Rightarrow 2\times 2\times 2\times 3=24$
This value is equal to d.
$\Rightarrow d=24$

Hence, the HCF or highest common factor of 48 and 72 which in turn is equal to d is given by 24.

Note: We need to know the prime factors method to solve this question. We can also solve this question by writing down all the factors of the two numbers and checking for the largest factor common between the two. This does not involve the use of any prime factors.