9 a) Find the prime factorization of 1350. b) Find D(1350). c) Find S(1350). d)

Question

9 a) Find the prime factorization of 1350. b) Find D(1350). c) Find S(1350). d) Find P(1350). e) Is 1350 abundant, deficient, or perfect? 10) Let k be a natural number. The number 2k-1(2k-1) isp 1) Label each of the following as true, false, or not knowr a) There are infinitely many prime numbers. b) There are infinitely many Mersenne primes. c) If an even number is perfect, it is of the form 2k-1 d) There are no odd perfect numbers. e) If 2k-1 is prime, then k is prime. f) If k is composite, then 2k-1 is composite. Give one prime factor of 36,893,488,147,419,103,23 he number 524,287 (which is 219-1) is prime. Wha erfect number? · 219 210(211-1) perfect? Why or why not? 26/27 1 rfect2 Whyor why not?

Explanation / Answer

1 + 3^1 + 3^2 + 3^3 = 19

1 + 5^1 + 5^2 = 31

now 675+450+270+225+150+135+90+75+54+50+45+30+27+25+18+15+10+9+6+5+3+2+1=2370

2350<1350 so, the number 1350 is Abundant

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