Question

Write all factors of 96.

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. 96
So, we have to write all such numbers which divide the number 96 completely.
We write prime factorization of the given number.
Prime factorization of\[96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3\]
\[ \Rightarrow \]2, 3 are factors of 96 …….… (1)
So we have these prime numbers as its factors.
Also, 1 is a factor of every number.
\[ \Rightarrow \]1 is a factor of 96 …….… (2)
Similarly, we know every number is a factor of itself
\[ \Rightarrow \]96 is a factor of 96 …..… (3)
Now from the prime factorization we calculate the possible factors of 96 by pairing the prime factors.
\[2 \times 2 = 4\] is a factor of 96
\[2 \times 2 \times 2 = 8\] is a factor of 96
\[2 \times 2 \times 2 \times 2 = 16\] is a factor of 96
\[2 \times 2 \times 2 \times 2 \times 2 = 32\] is a factor of 96
\[2 \times 3 = 6\] is a factor of 96
\[2 \times 2 \times 3 = 12\] is a factor of 96
\[2 \times 2 \times 2 \times 3 = 24\] is a factor of 96
\[2 \times 2 \times 2 \times 2 \times 3 = 48\] is a factor of 96
\[ \Rightarrow \]4, 8, 16, 32, 6, 12, 24 and 48 are factors of 96. ……...… (4)
So, from equations (1), (2), (3) and (4): 96 has factors 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96.

\[\therefore \]The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96.

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.