Question

Write all the factors of the following number: \[36\]

Answer 1

Hint: The given question requires us to find out the factors of given number. A number's factor is defined as a number that divides the original number evenly or precisely. Each prime number has only two factors: 1 and the number itself, while each composite number has more than two factors, which will include prime factors.

Complete step-by-step answer:
An algebraic expression's factors are the values that can be used to divide the given expression. Fractions are not considered to be factors of a given expression. Negative numbers are also included in factors since the product of two negative numbers is a positive number.
We can find out the factors of a given number by various methods. Let us find the factors of \[36\] with different methods.

Method 1: Use multiplication tables in case of small numbers.
With the help of the multiplication table, we have to find all the numbers whose product will be \[36\] . Hence, we will get:
 \[6 \times 6 = 36\]
 \[2 \times 3 \times 2 \times 3 = 36\]
Moreover, \[18 \times 2 = 36\] , \[9 \times 4 = 36\] and \[12 \times 3 = 36\]
Therefore,
Positive factors of \[36\] are \[1,2,3,4,6,9,12,18\] and \[36\] &
Negative factors are \[ - 1, - 2, - 3, - 4, - 6, - 9, - 12, - 18\] and \[ - 36\] .

Method 2: Using division method
In this case, the number is divided by prime numbers till we get a quotient in the prime number or \[1\] .
Here \[36\] is divided by prime numbers to arrive at the solution and all the quotients will form the factor of \[36\] . Moreover, the product of divisor will also form part of factor i.e. \[2 \times 2 = 4\] , \[3 \times 2 = 6\] , \[3 \times 3 = 9\] and \[2 \times 3 \times 2 = 12\] .
Therefore,
Positive factors of \[36\] are \[1,2,3,4,6,9,12,18\] and \[36\] &
Negative factors are \[ - 1, - 2, - 3, - 4, - 6, - 9, - 12, - 18\] and \[ - 36\] .

Method 3: Prime Factorization Method
 \[36\] can be written in form of prime factors as:
 \[2 \times 2 \times 3 \times 3 = 36\]
Now we just have to multiply the multiples i.e. \[2 \times 2 = 4\] , \[3 \times 2 = 6\] , \[3 \times 3 = 9\] and \[2 \times 3 \times 2 = 12\] .
Hence,
Positive factors of \[36\] are \[1,2,3,4,6,9,12,18\] and \[36\] &
Negative factors are \[ - 1, - 2, - 3, - 4, - 6, - 9, - 12, - 18\] and \[ - 36\] .

Note: In case of large numbers, division method is preferable.
In the given question, we can write positive factor pair of \[36\] as follows:
 \[(1,36),(2,18),(3,12),(4,9),(6,6)\]
We can write negative factors in a similar manner.