Question

If $10800=2^a\times 3^b\times 5^c$ then find the value of a, b and c.

• A. $a=3,b=3,c=2$
• B. $a=4,b=2,c=2$
• C. $a=1,b=3,c=2$
• D. $a=4,b=3,c=2$

Answer 1

The correct option is D

$a=4,b=3,c=2$

Given

$10800=2^a\times 3^b\times 5^c$

10800 can be written as a product of its primes as follows

10800 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5

$\Rightarrow 2^4\times 3^3\times 5^2$

$\therefore 2^4\times 3^3\times 5^2=2^a\times 3^b\times 5^c$

$\Rightarrow a=4,b=3,c=2$