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7776

7776 is a natural number that follows 7775 and precedes 7777. In decimal notation it is written as 7,776.

Mathematical properties: 7776 is a perfect fifth power, since it equals 6^5. Its prime factorization is 2^5

Base representations and divisibility: In base 6, 7776 equals 100000_6 because 6^5 = 7776. In base 10

Context and significance: As 6^5, 7776 represents the number of possible ordered 5-tuples drawn from a set

In summary, 7776 is notable for being a fifth power with a simple prime factorization, a clean

·
3^5,
or
(2
·
3)^5.
Therefore
it
has
(5
+
1)(5
+
1)
=
36
positive
divisors.
The
number
can
be
expressed
as
the
product
of
two
fifth
powers,
namely
32
×
243.
its
digits
sum
to
7
+
7
+
7
+
6
=
27,
so
7776
is
divisible
by
27
(and
by
9,
3,
and
81
as
well,
due
to
its
factorization
2^5
·
3^5).
It
can
also
be
written
as
32
×
243,
highlighting
its
divisibility
by
powers
of
2
and
3.
of
6
elements.
This
makes
it
a
natural
example
in
discussions
of
exponentiation
and
combinatorial
counting.
It
is
not
an
HCN
(highly
composite
number)
since
smaller
integers
already
achieve
the
same
or
greater
divisor
counts.
base-6
representation,
and
its
role
in
counting
with
finite
alphabets.