In this section we will discuss how to calculate HCF/GCD of numbers given in fraction or decimal form.

Solving HCF of regular number is straightforward but if numbers are in form of decimals, you need different technique to solve the problem.

The **formula for HCF of Fraction** is written as:

Please remember this formula as with its help we are going to solve related questions.

## Solved Examples of HCF of Fractions and Decimals

(**01) Find HCF of 0.63, 1.05 and 2.1**

**Solution**

The numbers are in Decimal Form.

In order to solve this type of question, do the following steps:

**Step 01:**

Convert the decimal into fractions form such that the number of digits in denominator is same

0.63 ⟹ 63/100

1.05 ⟹ 105/100

2.1 ⟹ 210/100

**Step 02:**

Now use the HCF fraction formula**HCF of Fraction = HCF of numerator / LCM of denominator**

**HCF of NUMERATOR**

HCF (63,105,210)

Using Prime Factorization Method

Hence, **HCF (63, 105,210) ⟹ 21** —-(1)

**LCM of DENOMINATOR**

The denominators are 100, 100, 100

LCM(100,100,100) ⟹ 100 —(2)

Now Putting (1) and (2) in HCF Formula we get

HCF (0.63, 1.05, 2.1) ⟹ 21/100 ⟹ 0.21

**Hence 0.21 is the answer**

**(02) Find HCF of** \mathtt{\frac{9}{10} ,\ \frac{12}{25} ,\ \frac{18}{35} \ \&\ \frac{21}{40} \ } .

**Solution****Step 01:**

Find HCF of numerators.

Calculating HCF (9, 12, 18, 21)

Hence, HCF (9,12, 18, 21) ⟹ **3** — (1)

**Step 02:**

Find LCM of denominator.

Calculating LCM (10, 25, 35, 40) using common division method

Hence, LCM (10, 25, 35, 40) ⟹ **1400** —–(2)

**Step 03:**

Putting (1) and (2) in HCF Fraction Formula we get,

**HCF (9/10, 12/25, 18/35, 21/40)** ⟹** 3/1400**

**Hence 3/1400 is the right answer**

**(03) Find HCF of 1.08, 0.36 and 0.9**

**Solution**

Numbers are in decimal form.

Follow the below steps;**Step 01:**

Convert all decimals into fraction such that all have same denominator.

1.08 ⟹ 108/100

0.36 ⟹ 36/100

0.9 ⟹ 90/100**Step 02:**

Find HCF of numerators (108, 36, 90)

Calculating HCF using Prime Factorization Method

Hence, HCF (108, 36, 90) ⟹ **18**

**Step 03:**

Find LCM of denominators**LCM (100,100,100) = 100**

**Step 04**:

Putting values in HCF formula.

HCF of Fraction = HCF of numerator/ LCF of Denominator

HCF = 18/100

HCF = 0.18

**Hence 0.18 is the answer**

**(04)** Find HCF of \mathtt{\frac{2}{3} ,\ \frac{8}{9} ,\ \frac{64}{81} \ \&\ \frac{10}{27} \ }

**Solution**

Numbers are in Fraction format.

We will use the formula;

\mathtt{HCF\ ( Fraction) =\ \frac{HCF\ of\ numerator}{LCM\ of\ denominator}} **Step 01****Find HCF of numerator**

HCF = (2, 8, 64, 10)

Calculating prime factors of numbers;

\mathtt{2\ \Longrightarrow \ 2}\\\ \\ \mathtt{8\ \Longrightarrow \ 2^{3}}\\\ \\ \mathtt{64\Longrightarrow \ 2^{6}}\\\ \\ \mathtt{10\ \Longrightarrow \ 2\times 5}

Number 2 is only common element.

Hence, HCF (2, 8, 64, 10) is **2**

**Step 03****Find LCM of denominators.**

LCM (3, 9, 81, 27)

Calculating individual factors.

\mathtt{3\ \Longrightarrow \ 3}\\\ \\ \mathtt{9\ \Longrightarrow \ 3^{2}}\\\ \\ \mathtt{81\Longrightarrow \ 3^{4}}\\\ \\ \mathtt{27\ \Longrightarrow \ 3^{3}}\

Highest value of 3 is \mathtt{3^{4}} .

Hence, LCM (3, 9, 81, 27) = 81

**Step 05****Putting the values of HCF and LCM in formula**.

HCF (fraction) = HCF (numerator) /LCM denominator

HCF (fraction) = 2/81

**Hence, 2/81 is the required solution.**

**(05) Find HCF/GCD of 1.75, 5.6 and 7**

**Solution**

Numbers are in decimal form.

**Step 01:**

Convert the decimals into fractions with same denominator.

1.75 ⟹ 175/100

5.6 ⟹ 560/100

7 ⟹ 700/100

**Step 02:**

Find HCF of numerators.

Hence, HCF (175, 560, 700) ⟹ **35** ——(1)

**Step 03**

Find LCM of denominators.

LCM (100,100,100) = 100 – – – eq(2)

**Step 04**

Now putting values of (1) and (2) in HCF formula we get

HCF (1.75, 5.6, 7) ⟹ 35/100 ⟹ 0.35

Hence 0.35 is the required HCF of the above question

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