Question
Using prime factorization, find the $HCF$ and $LCM$ of:
$396, 1080$
$396, 1080$
✓
Answer
$396 = 2 \times 2 \times 3 \times 3 \times 11 $
$= 2^2 \times 3^2\times 11 1080 $
$= 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 5 $
$= 2^3 \times 3^3 \times 5$
HCF $(396, 1080)$
$ = 2^2 \times 3^2$
$=36$LCM $(396, 1080) $
$= 2^3 \times 3^3 \times 11 \times 5$
$ =11880$
HCF $\times $ LCM
$= 427680 144 \times 198$
$ = 427680$
$\Rightarrow $ HCF $\times $ LCM = product of given numbers Hence verified.
$= 2^2 \times 3^2\times 11 1080 $
$= 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 5 $
$= 2^3 \times 3^3 \times 5$
HCF $(396, 1080)$
$ = 2^2 \times 3^2$
$=36$LCM $(396, 1080) $
$= 2^3 \times 3^3 \times 11 \times 5$
$ =11880$
HCF $\times $ LCM
$= 427680 144 \times 198$
$ = 427680$
$\Rightarrow $ HCF $\times $ LCM = product of given numbers Hence verified.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If three consecutive vertices of a parallelogram are (1, -2), (3, 6) and (5, 10), find its fourth vertex.
A father is three times as old as his son. After twelve years, his age will be twice as that of his son then. Find their present ages.
From an external point P, tangents PA and PB are drawn to a circle with centre O. If CD is the tangent to the circle at a point E and PA = 14cm, find the perimeter of $\triangle\text{PCD}.$
→In the adjoining figure, chord AD $\cong$ chord BC. m(arc ADC) = 100°, m(arc CD) = 60°. Find m(arc AB) and m(arc BC).
→A cone of maximum size is carved out from a cube of edge 14cm. Find the surface area of the cone and of the remaining solid left out after the cone carved out.
Short-Answer Questions:
Show that $\frac{\sqrt2}{3}$ is irrational.
→Show that $\frac{\sqrt2}{3}$ is irrational.
Find the coordinates of the midpoint of the line segment joining P(0,6)and Q(12,20).
Draw a circle with centre M and diameter 6 cm. Draw a tangent to the circle from a point N at distance of 9 cm from the centre.
In an A.P., if the $5^{\text {th }}$ and 12 th terms are 30 and 65 respectively, what is the sum of the first 20 terms.
→Draw a tangent to a circle of radius 3 cm and centre 'O' at any point 'K' on the circle.