Question

If the product of first 10 natural numbers is 2 power a× 3 power b × 5 power c × 7 power d find the value of a+b+c+d

Answer 1

$\textbf{Given:}$

$\text{The product of first 10 natural numbers}$

$\mathrm{=2^a{\times}3^b{\times}5^c{\times}7^c}$

$\textbf{To find:}$

$\text{The value of a+b+c+d}$

$\textbf{Solution:}$

$\text{Consider,}$

$\mathrm{1{\times}2{\times}3{\times}4{\times}5{\times}6{\times}7{\times}8{\times}9{\times}10=2^a{\times}3^b{\times}5^c{\times}7^d}$

$\mathrm{2{\times}3{\times}2^2{\times}5{\times}(2{\times}3){\times}7{\times}2^3{\times}(3{\times}3){\times}(2{\times}5)=2^a{\times}3^b{\times}5^c{\times}7^d}$

$\mathrm{2^8{\times}3^4{\times}5^2{\times}7^1=2^a{\times}3^b{\times}5^c{\times}7^d}$

$\text{Equating powers, we get}$

$\text{a=8,b=4,c=2,d=1}$

$\text{Now}$

$\mathrm{a+b+c+d}$

$\mathrm{=8+4+2+1}$

$\mathrm{=15}$

$\textbf{Answer:}$

$\textbf{The value of a+b+c+d is 15}$

Answer 2

Answer:

same 23456688999988877666654322123457890853212579u