Question

The sum of non-prime positive divisors of $450$ is

• A. $1209$
• B. $1299$
• C. $1199$
• D. $1099$

Answer 1

The correct option is C $1199$

Prime factors of $450$, is $2\times 3\times 3\times 5\times 5$, now non-prime divisors will be combinations of these.

when two are multiplied, $2\times 3=6,2\times 5=10,3\times 3=9,3\times 5=15,5\times 5=25$

when three are multiplied, $2\times 3\times 3=18,2\times 3\times 5=30,2\times 5\times 5=50,3\times 3\times 5=45,3\times 5\times 5=75$

when four are multiplied, $2\times 3\times 3\times 5=90,2\times 3\times 5\times 5=150,3\times 3\times 5\times 5=225$

when four are multiplied, $2\times 3\times 3\times 5\times 5=450$

Also $1$ is also a non-prime divisor,

Sum of divisors $=1198+1=1199$