Question

Express the following number as a product of its prime factors using tree method.
$140$

Answer 1

Hint: Expressing a number is another form of representation of the same number. In this problem we are required to express our number as a product of various prime factors such as 2,3,5 and so on having no occurrence of a composite number.

Complete step-by-step answer:

A prime number is a natural number greater than 1 that is not a product of a combination of other natural numbers. In other words, a number which is either divisible by itself (i.e. the same number) or divisible by 1 is called a prime number. For example, numbers such as 2, 3, 5, 7 and so many others are prime numbers as the multiples of 2 are (1,2). So, these numbers are completely divisible by two natural numbers only.
A composite number is a natural number which can be expressed as a product of more than two natural numbers. In simple words, all the numbers other than prime numbers and 1 are composite numbers. For example, numbers such as 4, 6, 9 and others are composite numbers as the multiples of 4 are (1,2,4), multiples of 6 are (1,2,3,6).
1 is neither prime nor composite.
Factors of a number are those numbers that can be multiplied together to make another number. For example, 2 and 4 are a factor pair of 8. A factor which is prime in its value is called prime factors. In other words, prime numbers that can be multiplied to obtain the original number are called prime factors of a number.
So, to express 140:
$\begin{align}
  & 140=2\times 70 \\
 & 140=2\times 2\times 35 \\
 & 140=2\times 2\times 5\times 7 \\
\end{align}$
So, the prime factors of 140 are (2,5,7) and the product can be expressed as $140=2\times 2\times 5\times 7$.

Note: 1 is neither a prime number nor a composite number. One should have thorough knowledge about prime numbers to solve these types of questions. The common mistake that students commit is by writing 1 in the product as well. It is also important to note that the prime factors include only the unique numbers while expressing a number as a product of primes involves repetitions as well.