Question

How do write $ 140 $ as the product of its prime factors?

Answer 1

Hint: In this question, we need to write $ 140 $ as the product of its prime factors. Here, we will determine the factors of $ 140 $ , then we will determine the prime factors of $ 140 $ , using the method of prime factorization.

Complete step-by-step answer:
Here, we need to write $ 140 $ as the product of its prime factors.
We know that $ 140 $ is a composite number.
Therefore, the possible factors of $ 140 $ are
$ 1 \times 140,2 \times 70,4 \times 35,5 \times 28,7 \times 20,10 \times 14 $ .
Prime factorization is a method of finding prime numbers which multiply to make the original number.
A prime number is a natural number greater than $ 1 $ that is not a product of two smaller natural numbers.
In prime factorization, we start dividing the number by the first prime number $ 2 $ and continue to divide by $ 2 $ until we get a decimal or remainder. Then divide by $ 3,5,7,... $ etc. until we get the remainder $ 1 $ with the factors as prime numbers. Then write the numbers as a product of prime numbers.
Thus, $ 140 $ as the product of its prime factors is,
  $ 140 = 2 \times 2 \times 5 \times 7 $
This can be also written in exponential form as,
  $ 140 = {2^2} \times 5 \times 7 $
So, the correct answer is “ $ {2^2} \times 5 \times 7 $ ”.

Note: In this question it is important to note here that a composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than $ 1 $ and itself. However, the prime factorization is also known as prime decomposition. And, the prime factorization of the prime number is the number itself and $ 1 $ . Every other number can be broken down into prime number factors, but the prime numbers are the basic building blocks of all the numbers.