Question

How many factors does $144$ have ?

Answer 1

Hint: They have asked for factors of $144$ , which means factors are nothing but the numbers which divides the given number with zero remainder. We can use the factorization method to find the factors of the given number.

Complete step-by-step answer:
Here they have asked for factors of $144$ , where factors are nothing but the numbers which divide the given number with zero remainder.
We can use the factorization method to find the factors of the given number. Or we can simply divide the given number by all the numbers till the given number to get the factors of the given number that is $144$ .
We can calculate the factors by division method as follows:
The following are the factors of the number $144$ with remainder zero.
$144 \div 1 = 144$ with zero remainder.
$\
  144 \div 2 = 72 \\
  144 \div 3 = 48 \\
  144 \div 4 = 36 \\
  144 \div 6 = 24 \\
  144 \div 8 = 18 \\
  144 \div 9 = 16 \\
  144 \div 12 = 12 \\
  144 \div 16 = 9 \\
  144 \div 18 = 8 \\
  144 \div 24 = 6 \\
  144 \div 36 = 4 \\
  144 \div 48 = 3 \\
  144 \div 72 = 2 \\
  144 \div 144 = 1 \\
\ $
Therefore the factors of the number $144$ are $1,2,3,4,6,8,9,12,16,18,24,36,48,72$ and $144$.
The above factors are positive factors of $144$. But we can also have the negatives as well because if we multiply two negative numbers the resultant number will be positive. So whatever we have as positive factors the same can be converted to negative factors.
Therefore we have $15$ positive factors and $15$ negative factors. So there are a total of $30$ factors.

Note: Here we have mentioned a total of $30$ factors only because they have not asked for only positive or negative they have just asked the factors, so we have included both. If they ask separately then there is no need to consider both.