# HCF Questions (Level 01)-Part 1

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

(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.

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

(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