Find the HCF of 1008 and 1080 by prime factorization method.

Question:

Find the HCF of 1008 and 1080 by prime factorization method.

 

Solution:

Prime factorisation:

$1008=2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 7=2^{4} \times 3^{2} \times 7$

$1080=2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 5=2^{3} \times 3^{3} \times 5$

HCF = Product of  smallest power of each common prime factor in the number

$=2^{3} \times 3^{2}=72$

 

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