Question

2520=2^3×3^2×5×7,3960 =2^3×3^2×5×11, 4725= 3^3×5^2×7.If a^x.b^y is the H.C.F of the given numbers then the value of x+y is

please send me answer.

Answer 1

$2520 = {2}^{3} \times {3}^{2} \times 5 \times 7 \\ 3960 = {2}^{3} \times {3}^{2} \times 5 \times 11$
$4725 = {3}^{3} \times {5}^{2} \times 7$
HCF of given number =
${3}^{2} \times 5 = (9 \times 5) = 45$
as per question , if
${a}^{x} {b}^{y}$
then find the value of x+y
$x = {3}^{2} \\ y = {5}^{1} \\ x + y = (2 + 1) = 3$