# 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. Here on this page of How To Solve HCF Questions Quickly you will come across methods that will help you to reduce your time to solve such questions.

### 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.

### Factorization Method:

#### Express each one of the given numbers as the product of prime factors. The product of least powers of common prime factors gives H.C.F.

Question – Find out the HCF of 60 and 75.

Answer -Let us express each number as a product of prime factors.

60 = 2× 2 × 3 × 5

75 = 3 × 5 × 5

HCF is the product of all common prime factors using the least power of each common prime factor.

Here, common prime factors are 3 and 5

The least power of 3 here = 3

The least power of 5 here = 5

Hence, HCF = 3 × 5 = 15

### Division Method:

Suppose we have to find the H.C.F. of two given numbers, divide the larger by the smaller one. Now, divide the divisor by the remainder. Repeat the process of dividing the preceding number by the remainder last obtained till zero is obtained as remainder. The last divisor is required H.C.F.

Example 1: Find out HCF of 60 and 75.

Let us use division method to solve this question.

Hence HCF of 60 and 75 = 15

### Dividing the numbers:-

Step 1: Write the given numbers in a horizontal line separated by commas.

Step 2: Divide the given numbers by the smallest prime number (write in the left side) which can exactly divide all the given numbers.

Step 3: Write the quotients in a line below the first.

Step 4: Repeat the process until we reach a stage where no common prime factor exists for all the numbers.

Step 5: We can see that the factors mentioned in the left side clearly divide all the numbers exactly and they are common prime factors.

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 divisor 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. The two numbers are 24 and a, whose 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:     As we know the HCF x LCM = product of two numbers = 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 Questions Quickly 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 = $\frac{1}{1}$

= 1