Question

Write all factors of 64.

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. 64
So, we have to write all such numbers which divide the number 64 completely.
We write prime factorization of the given number.
Prime factorization of \[64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2\]
\[ \Rightarrow \]2 is a factor of 64 ………..… (1)
So we have these prime numbers as its factors.
Also, 1 is a factor of every number.
\[ \Rightarrow \]1 is a factor of 64 ……….… (2)
Similarly, we know every number is a factor of itself
\[ \Rightarrow \]64 is a factor of 64 …….… (3)
Now from the prime factorization we calculate the possible factors of 64 by pairing the prime factors.
\[2 \times 2 = 4\] is a factor of 64
\[2 \times 2 \times 2 = 8\] is a factor of 64
\[2 \times 2 \times 2 \times 2 = 16\] is a factor of 64
\[2 \times 2 \times 2 \times 2 \times 2 = 32\] is a factor of 64
\[ \Rightarrow \]4, 8, 16 and 32 are factors of 64. …….… (4)
So, from equations (1), (2), (3) and (4): 64 has factors 1, 2, 4, 8, 16, 32 and 64.

\[\therefore \]The factors of 64 are 1, 2, 4, 8, 16, 32 and 64.

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.