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HCF

Highest Common Factor (HCF)

Methods of Finding the HCF

There are two methods of find the HCF which have been described as follows

1. Prime Factorisation Method

e.g. If we are to determine the HCF of 12, 18 and 24.

2 and 3 are common.

∴ Required HCF = 2 × 3 = 6

Note : we choose those factors which are common to all the numbers.

2. Division Method

Step I : Divide the larger number by smaller number.
Step II : Divide the divisor by the remainder.
Step III : Repeat step II till the remainder becomes zero. Now, the last divisor would be the required HCF.

e.g. If we are to determine the HCF of 12, 18 and 27.

Step - 1 : 12 and 18

Step - 2 : 6 and 27

Finally,

The last divisor is 3.

∴ The required HCF is 3.

HCF and LCM of Fractions

$\mathbf{\textrm{LCM of Fractions}=\frac{\textrm{LCM of Numerators}}{\textrm{HCF of Denominators}}}$

$\mathbf{\textrm{HCF of Fractions}=\frac{\textrm{HCF of Numerators}}{\textrm{LCM of Denominators}}}$

$\mathbf{\textrm{Find the LCM of 1/2,3/2 and 9/4}}$

$=\frac{1}{2},\frac{3}{2}and\frac{9}{4}$

$=\frac{LCM of 1,3,9}{HCF of 2,2,4}$

$=\frac{9}{2}$

The product of LCM and HCF of 3/5 and 8/3.

HCF and LCM of Decimal Numbers

Steps to Find HCF/LCM of Decimal Numbers

Equalize the Decimal Places : Ensure all the decimal numbers have the same number of decimal places by adding zeros to the end of the numbers if necessary.
Remove the Decimal Points : Convert the decimal numbers to integers by removing the decimal points.
Find the HCF or LCM : Calculate the HCF or LCM of these integers as you would normally do.
Adjust for Decimal Places : Convert the result back to a decimal by placing the decimal point in the correct position.

Relation between LCM and HCF

If A and B are two numbers whose LCM and HCF are L and H, respectively, then

A x B = L x H

Product of numbers = Product of LCM and HCF