# How To Solve HCF Questions Quickly

## How to solve HCF Problems

The highest or greatest positive integer which divides each of the two or more numbers is called Highest Common Factor or Greatest Common Divisor i.e. HCF or GCD

### HCF: How to Solve HCF Questions Quickly.

• The Highest Common Factor (HCF) can be quickly solved using the long division method. The method simply requires division of the bigger number by the smaller number. The smaller number is then divided by the remainder obtained in the first division. This process is repeated until zero is obtained. The divisor generated in this case is the HCF of the number.

### Prime Factorization Method

• This is one of the simplest methods to calculate the HCF of a number. The following steps help to calculate HCF of a number.

a). Expand the given number as the product of their prime factors.

b). Check for common prime

The step can be best explained with the help of an example.

Question 1. Calculate the HCF of 248 and 492.

Options:

A.  10

B.  4

C.  20

D.  5

Solution:    We will follow the above-mentioned method to calculate the HCF of the given numbers.

We divide 492 by 248.

The devisor obtained at the end was 4

Therefore, the HCF of these numbers is 4.

It is also easy to determine a number when its LCM and HCF with another number is given.

Question 2. In the case of two numbers, 24 and a the HCF is 8, and the LCM is 48. What will be the value of a?

Options:

A.  16

B.  64

C.  2

D.  9

Solution:     HCF x LCM = 24 x a = 48 x 8

Therefore, a =16

If a number leaves the same remainder when it divides a set of numbers, it is easy to calculate it.

Question 3. If a number n leaves the same remainder when it divides 20, 50, and 62. What is the maximum possible value for n?

Options:

A.  8

B.  4

C.  6

D.  7

Solution:    The greatest number which will leave the same remainder is the HCF of

(62-20, 62-50, 50-20)

Or, we have to calculate the HCF of 42, 12, and 30

= 6

Therefore, the maximum value is 6.

### How To Solve Quickly HCF Questions by Calculating the HCF of Decimal Numbers

• Calculating HCF of decimal numbers is also an easy task. For this, you simply need to convert the decimal number into non-decimal number.

Question 4.Calculate the HCF of the given numbers 0.54, 0.06, and 1.08.

Options:

A.  1.08

B.  0.06

C.  2.01

D.  3.15

Solution:     These decimal numbers first need to be converted into non-decimal forms.

For this, all of these numbers must be multiplied by 100.

After multiplication, we get 54, 6, and 108.

Now, we can easily calculate the HCF of these numbers.

HCF of 54, 6, and 108 is 6.

Now, when we divide 6 by 100, we get 0.06.

### How To Solve HCF of Fractions

• Calculating the HCF of numbers in fractional form is simple. The method simply requires taking the HCF of all the numerators and denominators separately and dividing their result to get the answer.

Question 5. Find the HCF of $\frac{1}{2}, \frac{2}{3}, \frac{4}{5}, and \frac{6}{7}$.

Options:

A.  4

B.  1

C.  7

D.  3

Solution:  To calculate the HCF of the given fractions, first, calculate the HCF of numerator and denominator separately.

In the next step, these results are put into fractions to calculate the final result.

HCF of (1, 2, 4, 6) = 1

HCF of (2, 3, 5, 7) = 1

Resultant HCF = [/latex]\frac{1}{1}[/latex]

= 1