A number that has an odd number of factors and is smaller than 55
49 is smaller than 55 and its factors are 1,7, and 49. That's three and
3 is an odd number. So 49 is a number that has an odd number of factors and is
smaller than 55
36 is smaller than 55 and its factors are 1,2,3,4,6,9,12,18, and 36. That's
nine and 9 is an odd number. So 36 is also a number that has an odd number of
factors and is smaller than 55.
25 is smaller than 55 and its factors are 1,5, and 36. That's three and 3 is
an odd number. So 25 is also a number that has an odd number of factors and is
smaller than 55.
16 is smaller than 55 and its factors are 1,2,4,8, and 16. That's five and 5
is an odd number. So 16 is also a number that has an odd number of factors and
is smaller than 55.
9 is smaller than 55 and its factors are 1,3, and 9. That's three and 3 is an
odd number. So 9 is also a number that has an odd number of factors and is
smaller than 55.
4 is smaller than 55 and its factors are 1,2, and 4. That's three and 3 is an
odd number. So 4 is also a number that has an odd number of factors and is
smaller than 55.
1 is smaller than 55 and its only factor is 1. That's one and 1 is an odd
number. So 1 is also a number that has an odd number of factors and is smaller
than 55.
The interesting part of this is that the only positive integers that have an
odd number of factors are the perfect squares,
1²=1, 2²=4, 3²=9, 4²=16, 5²=25, 6²=36, 7²=49.
Perfect squares have an odd number of factors because factors come in pairs and
the square root of a perfect square is only one factor.
Edwin
