Question

The total number of factors of the number 144 is
a) 16
b)15
c)14
d) None of the above

Answer 1

a 16 ?...............

Answer 2

$Let's\ prime\ factorize\ 144\ by\ LCM\ method. \\ \\ 2\ |\underline{144} \\ 2\ |\underline{72} \\ 2\ |\underline{36} \\ 2\ |\underline{18} \\ 3\ |\underline{9} \\ 3\ |\underline{3} \\ 1\ |\underline{1} \\ \\ \therefore\ 144 = 2^4 \times 3^2$

$Here,\ 2^4\ has\ the\ power\ 4.\ Add\ 1\ to\ it. \\ \\ 4 + 1 = \bold{5} \\ \\ And\ 3^2\ has\ the\ power\ 2.\ Add\ 1\ to\ it\ also. \\ \\ 2 + 1 = \bold{3} \\ \\ Multiply\ both\ 5\ and\ 3. \\ \\ 5 \times 3 = \bold{15} \\ \\ 15\ got\ is\ the\ answer!$

$\\ \\ \\ \therefore\ 144 = 2^4 \times 3^2\ has\ 15\ factors,\ and\ that\ factors\ are: \\ \\ 1)\ 2^0 \times 3^0 = 1 \times 1 = \bold{1} \\ \\ 2)\ 2^0 \times 3^1 = 1 \times 3 = \bold{3} \\ \\ 3)\ 2^0 \times 3^2 = 1 \times 9 = \bold{9} \\ \\ 4)\ 2^1 \times 3^0 = 2 \times 1 = \bold{2} \\ \\ 5)\ 2^1 \times 3^1 = 2 \times 3 = \bold{6} \\ \\ 6)\ 2^1 \times 3^2 = 2 \times 9 = \bold{18} \\ \\ 7)\ 2^2 \times 3^0 = 4 \times 1 = \bold{4} \\ \\ 8)\ 2^2 \times 3^1 = 4 \times 3 = \bold{12}$

$\\ \\ 9)\ 2^2 \times 3^2 = 4 \times\ 9 = \bold{36} \\ \\ 10)\ 2^3 \times 3^0 = 8 \times 1 = \bold{8} \\ \\ 11)\ 2^3 \times 3^1 = 8 \times 3 = \bold{24} \\ \\ 12)\ 2^3 \times 3^2 = 8 \times 9 = \bold{72} \\ \\ 13)\ 2^4 \times 3^0 = 16 \times 1 = \bold{16} \\ \\ 14)\ 2^4 \times 3^1 = 16 \times 3 = \bold{48} \\ \\ 15)\ 2^4 \times 3^2 = 16 \times 9 = \bold{144}$

$\\ \\ \\ \therefore\ Option\ (B)\ is\ correct.$

$\\ \\ \\ Hope\ this\ may\ be\ helpful. \\ \\ Please\ mark\ my\ answer\ as\ the\ \bold{brainliest}\ if\ this\ may\ be\ helpful. \\ \\ Thank\ you.\ Have\ a\ nice\ day. \\ \\ \\ \#adithyasajeevan$