Question

Write all the factor of the following number: 21

Answer 1

Hint: We write the factors of the given number by writing the prime factorization of the given number. Form all possible factors by multiplying the prime factors with each other.
* Prime factorization of a number is writing the number in multiples of its factors where all factors are prime numbers.

Complete step-by-step answer:
We have to find all the possible factors of the given number i.e. 21
So, we have to write all such numbers which divide the number 21 completely.
We write prime factorization of the given number.
Prime factorization of\[21 = 3 \times 7\]
\[ \Rightarrow \]3, 7 are factors of 21 ………...… (1)
So we have these prime numbers as its factors.
Also, 1 is a factor of every number.
\[ \Rightarrow \]1 is a factor of 21 ………….… (2)
Similarly, we know every number is a factor of itself
\[ \Rightarrow \]21 is a factor of 21 ………...… (3)
So, from equations (1), (2) and (3): 21 has factors 1, 3, 7 and 21.

\[\therefore \]The factors of 21 are 1, 3, 7 and 21.

Note: Students may not write the number 1 as a factor as they might think only the numbers occurring in prime factorization are the factors of the given number, which is wrong. Keep in mind the numbers in prime factorization are only the prime factors, from multiplication of each prime factor to another prime factor we can form factors of the given number. Also, 1 divided every number in the number system so it is always a factor of the given number.