The only square number in that range that has 32 as a factor is 64.
Yes.
Since all integers have at least a common factor of 1, there is no integer that satisfies your request.
All numbers have factors. Some factors are perfect squares. We call these perfect square factors. 9 is a perfect square factor of 27.
Yes, because each factor must have another factor to go with it, but the square root of a number can have itself as a pair.
There are square numbers (numbers which are a square of an integer), such as 4. It's factors, listed are 1, 2, and 4. All square numbers have an odd number of factors. Then there's 1, which has only 1 factor: 1. All other numbers have an even number of factors. Prime numbers will have only 2 factors (2 is even).
Composite numbers have more than two factors.
One is a factor of all nonzero numbers.
All numbers with 12 as a factor have 2 as a factor, but not all have 10 as a factor.
The long but fool-proof way is to find the complete prime factorisation of the number. Then group all the factors into pairs, rejecting any that cannot be paired. The product of the numbers that are left is the largest square factor.
Yes. All even numbers have 2 as a factor.
2 is a divisor of all even numbers, and a divisor is a factor of all numbers which can be divided by it.
Yes. Factors are just numbers. All numbers have factors.