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COMEDK2018MathematicsBinomial Theorem

The sum of non-prime positive divisors of 450 is

Options

  1. A1209
  2. B1299
  3. C1199
  4. D1099

Correct answer

C. 1199

Step-by-step solution

Prime factors of 450 is 2 3 3 5 5 . Now, non-prime divisors will be combinations of these. When two are multiplied, 2 3=6,2 5=103 3=9,3 5=15,5 5=25 When three are multiplied, 2 3 3=18,2 3 5=30,2 5 5 =50 , 3 3 5=45,3 5 5=75 When four are multiplied, aligned &2 3 3 5=90,2 3 5 5=150 &3 3 5 5=225 aligned When five are multiplied, 2 3 3 5 5=450 Also, 1 is also a non-prime divisor. So, sum of divisors array r =9+15+25+30+50+45+75+90 +150+225+450+1=1199 array

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