Find the number:

Number Theory Level 2

If a,b,c are three positive integers and a^3 * b = a * b * c = 180 , then find c.


The answer is 1.

Yatish Pathak by Yatish Pathak , 33, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

4 solutions

Yatish Pathak
Apr 17, 2014

Since, 180 = 2^2 * 3^2 * 5 and a, b, c are integers. So, a must be 1. Therefore, b = 180 and hence c is 1.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

according to the question.... it is given (a^3) (b) = (a)(b)(c) = 180 OR it is same as (a^3) (b) = 180 = (a)(b)(c)
divide whole by (a)(b)
then a^2 = 180/ab = c...........(1)
also It evident from question that (a^3)(b) = 180
this condition is satisfied only if c=1 in eqn (1)
Hence c=1



0 Helpful 0 Interesting 0 Brilliant 0 Confused

a^3 b=a b c=180 c=180/a^3 b=180/a b a^2=1 a=1 and a^3 b=180 b=180 c=1

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Moshiur Mission
Apr 18, 2014

Since, 180 = 2 2 3 3 5 and a, b, c are integers. So, a=c=1& b = 180

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...