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.