Using prime factorization, find the HCF and LCM of: 1152, 1664 - Vidyadip

Question

Using prime factorization, find the HCF and LCM of:
$1152, 1664$

✓

Answer

$1152=2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3$
$=2^7 \times 3^2$
$1664=2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2=2^7$
$=128$
$\operatorname{HCF}(1152,1664)$
$=2^7$
$=128$
LCM $(1152,1664)$
$=2^7 \times 3^2 \times 13$
$=14976$
$\text { HCF } \times \text { LCM }=19169281152 \times 1664$
$=1916928$
$\Rightarrow H C F \times \text { LCM }$
$=$ product of given numbers Hence verified.

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