Question

if 7^3 2^7 and 9^3 are factors of a number denoted by (a*2^6*91*81) then what is the smallest possible value of 'a'?​

Answer 1

Answer:882

Step-by-step explanation:

(a*(2^6)*7*23*(3^4))  /   (7^2)*(2^7)*(3*6)

by solving this we can

Answer 2

Given :- if 7^3 2^7 and 9^3 are factors of a number denoted by (a*2^6*91*81) then what is the smallest possible value of 'a' ?

Solution :-

lets see prime factors of given number :-

→ a * 2⁶ * 91 * 81

→ a * 2⁶ * 7 * 13 * 9²

Now, we have given that, 7^3 , 2^7 and 9^3 are factors of given number.

to need least value of a , let us assume that, quotient is 1 .

Than,

→ (7³ * 2⁷ * 9³) * 1 = a * 2⁶ * 7 * 13 * 9²

now, as we can see :-

• if 7³ divide RHS completely, we need 7² .
• if 2⁷ divide RHS completely, we need 2.
• if 9³ divides RHS completely, we need 9 .

therefore,

→ Least value of a = 7² * 2 * 9 = 49 * 18 = 882 (Ans.)

Hence, Least value of a is 882.

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