MATH 135
Fall 2007
Assignment #5
Due: Wednesday 24 October 2007, 8:20 a.m.
HandIn Problems
1. (a) Convert (84 808)
9
to base 10. Show your work.
(b) Convert 37 390 to base 16, using
A
for ten,
B
for eleven,
C
for twelve,
D
for thirteen,
E
for fourteen, and
F
for ﬁfteen. Show your work.
2. Add and multiply the numbers (3157)
8
and (445)
8
, expressing your answers in base 8.
3. (a) Determine the prime factorizations of 39 204 000 and 9 922 500.
(b) Determine gcd(39 204 000
,
9 922 500) and lcm(39 204 000
,
9 922 500).
(c) Determine the number of positive divisors of 9 922 500.
(d) Determine the number of positive common divisors of 39 204 000 and 9 922 500 that are
multiples of 10.
4. A positive integer
n
is called a perfect square if
n
=
m
2
for some positive integer
m
.
(a) If
n
is a perfect square and
n
has prime factorization
n
=
p
c
1
1
· · ·
p
c
k
k
, prove that
c
1
,c
2
,...,c
k
are all even.
(b) Suppose that
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 Spring '09
 MARSHMAN
 Math, Algebra, Natural number, Prime number, positive common divisors

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