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Home » 1. Define HCF of two positive integers and find the HCF of the following pairs of numbers:
1. Define HCF of two positive integers and find the HCF of the following pairs of numbers:
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1. Define HCF of two positive integers and find the HCF of the following pairs of numbers:

(i)

    \[\mathbf{32}\text{ }\mathbf{and}\text{ }\mathbf{54}\]

(ii)

    \[\mathbf{18}\text{ }\mathbf{and}\text{ }\mathbf{24}\]

Solution:

Now, apply Euclid’s Division Lemma on

    \[54\text{ }and\text{ }32\]

    \[54\text{ }=\text{ }32\text{ }x\text{ }1\text{ }+\text{ }22\]

Since remainder

    \[\ne \text{ }0\]

, apply division lemma on

    \[32\]

 and remainder

    \[22\]

    \[32\text{ }=\text{ }22\text{ }x\text{ }1\text{ }+\text{ }10\]

Since remainder

    \[\ne \text{ }0\]

, apply division lemma on

    \[22\]

and remainder

    \[10\]

    \[22\text{ }=\text{ }10\text{ }x\text{ }2\text{ }+\text{ }2\]

Since remainder

    \[\ne \text{ }0\]

, apply division lemma on

    \[10\]

and remainder

    \[2\]

    \[10\text{ }=\text{ }2\text{ }x\text{ }5\text{ }+\text{ }0\]

Therefore, the H.C.F. of

    \[32\text{ }and\text{ }54\text{ }is~\mathbf{2}\]

Solution:

Now, apply Euclid’s Division Lemma on 

    \[24\text{ }and\text{ }18\]

    \[24\text{ }=\text{ }18\text{ }x\text{ }1\text{ }+\text{ }6.\]

Since remainder

    \[\ne \text{ }0\]

, apply division lemma on divisor

    \[18\]

and remainder

    \[6\]

    \[18\text{ }=\text{ }6\text{ }x\text{ }3\text{ }+\text{ }0.\]

Therefore, H.C.F. of 

    \[18\text{ }and\text{ }24\text{ =}~\mathbf{6}\]

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