Question

How to find the prime factorization of 221?

Answer 1

Hint:First of all we should know about the prime factorization. Prime factorization is the process in which we factories a number in the terms of prime numbers i.e. the factors will be prime numbers. These numbers is when multiplied by any natural numbers, then we get composite numbers.

Step by step answer:
Prime factorization is a method which is mainly used to “break down” or writing a given number as a product of prime numbers. In a case when a prime number occurs more than once then, it is generally expressed in the form of exponential.

Method 1 - Try prime factors in ascending order

a. Since, 221 is not divisible by 2 thus its last digit is odd.
b. Since, 221 is not divisible by 3 thus the sum of its digits is not.
c. Since, 221 is not divisible by 5 thus its last digit is neither 5 nor 0.
d. Since, 221 is not divisible by 7, thus \[221\, = \,210\,\, + \,\,11\],
Where  $210\, = \,3\, \times \,7\, \times \,10$ is divisible by the 7 but is not divisible by 11.
e. Since, 221 is not divisible by 11, thus $221\, = \,220\, \times \,1\,\, = \,\,2 \times \,10\, \times \,1\, + \,1$
f. Since, 221 is divisible by 13 and we find  $221\, = \,13\, \times \,17$

Note: In the process of prime factorization, we usually factorize a number into the prime numbers which are known as the prime factors. There are two methods which are Division method and Factor tree method. The way to find the prime factors of a composite number is Ladder method.