Question

What are the factors of 100 ?

Answer 1

Hint: When the term “factors” has been asked to find, then we will first break the number into its primes factors and then find all the possible factors of the number. This will not just give us the factors of 100, but also the smallest and largest factors of 100 along with the total number of factors.

Complete step-by-step answer:
We have been given to find the factors of 100. We will first find the prime factors of 100 by using the method of prime factorization. The number 100 can be then written as a product of its prime factors. This can be done as follows:
$\Rightarrow 100=2\times 2\times 5\times 5$
From the prime factorization of 100, we see that it consists of two 2’s and two 5’s . We will use all the possible combinations of these four numbers to find the factors of 100. This can be done as follows:
Let us represent the factors of 100 as ${{f}_{1}},{{f}_{2}},{{f}_{3}},{{f}_{4}}.......$
Where the first factor of 100 is a universal factor of any whole number, that is, 1 . Thus, the factors are:
$\begin{align}
  & \Rightarrow {{f}_{1}}=1 \\
 & \Rightarrow {{f}_{2}}=2 \\
 & \Rightarrow {{f}_{3}}=5 \\
 & \Rightarrow {{f}_{4}}=2\times 2=4 \\
 & \Rightarrow {{f}_{5}}=2\times 5=10 \\
 & \Rightarrow {{f}_{6}}=2\times 2\times 5=20 \\
 & \Rightarrow {{f}_{7}}=5\times 5=25 \\
 & \Rightarrow {{f}_{8}}=2\times 5\times 5=50 \\
 & \Rightarrow {{f}_{9}}=2\times 2\times 5\times 5=100 \\
\end{align}$
Hence, the factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50 and 100.

Note: The factors of an even number is not always an even number. But the factors of an odd number are always odd except for 1 which is neither odd nor even. Also, from our above calculation of factors, we see that the largest factor of a number is the number itself as factors of a number cannot exceed the number itself and the smallest factor of a number is always equal to the universal factor, that is, one.