How Many Factors Does 36 Have

Introduction

There are a total of 9 factors of the number 36. How do we calculate that? To get the answer to this query, it is necessary to first understand what "factors" and "multiples" of a number mean. As a result, you are aware of the multiplication facts. Every multiplication table is essentially a table containing the factors and multiples of the numbers. You might come across some similar variables and multiples among these diverse number multiples. Some numbers will only have the number 1 in common. Is this not true? Let's delve more into the idea of factors.

What is a Factor?

Suppose we have a multiplication table in which we find that the number A is equal to the product of another number a and the number b. The mathematical expression looks like the following.

\begin{align}A= a\times b \end{align}

Note that if we divide the number A by a, or b, we find that A is completely divisible by a and b.

\begin{align} A\div a=b \\ A\div b=a \end{align}

So, we deduce that both a and b are the factors of the number A.

Thus, we get that whenever an integer divides any number completely leaving no remainder, we infer that the integer is the factor of that number.

What is Multiple?

Let us examine another multiplication statement where the number B is equal to the product of the numbers b and c which is expressed as the following.

\begin{align}B= b \times c\end{align}

Here, we can interpret that by multiplying the number b with another number c, we get the number B which is greater than both b and c.

So, we conclude that the number B is the multiple of both the numbers b and c.

Thus, we get that whenever an integer is multiplied by another integer, we infer that the resultant product which is also an integer is the multiple of both the first and the second integers.

The Factors of Thirty-Six

To find the factors of six we can follow any of the following two methods.

• In the first method, write all the possible multiplications in which any two integers are multiplied to obtain the product as six only.

\begin{align} 36=1\times 36 \\ =2\times 18 \\ =3\times 12 \\ =4\times 9 \\ =6\times 6 \end{align}

• In the second method, we can factorize the number 6 in the following way

\begin{align} 2\underline{\left| 36 \right.} \\ 2\underline{\left| 18 \right.} \\ 3\underline{\left| \quad 9 \right.} \\ 3\underline{\left| \quad 3 \right.} \\ \quad 1 \end{align}\]

In both methods, we get the following.

The factors of 36 are 1, 2, 3, 4, 6, 9, 12,18, and 36.

Thus, we can correctly count that there are nine factors of 36.

Interpretation of The Multiplication Operation

We know that multiplication gives us the product of numbers. So, we can interpret the multiplication operation in the following way.

• Both the multipliers and the multiplicands in the operation of multiplication denote the factors of the product.

• The product obtained from the process of multiplication is a multiple of both multiplier and multiplicand.

The Important Features of The Factors of 36

Here are some of the important features of the factors of 36.

• Factor 1 is neither a composite number nor a prime number.

• Factor 2 is revealed as the only even prime number.

• Factor 3 is the smallest odd prime number.

• Factors 4 and 36 are the perfect squares.

• Factor 6 is the smallest number that can be expressed as the product of two prime numbers.

• Factors 2 and 3 are co-prime to each other.

• The least common multiple among the factors of 36 is 36.

• The number 36 is the multiple of the factors 1, 2, 3, 4, 6, 9, 12,18, and 36.

Conclusion

• The multiplication tables deal with the factors and the multiples of the numbers.

• The number 36 is written as thirty-six in words.

• The factors help us to find out the highest common factor among any given set of numbers.

• The multiples help us to find out the least common multiple among any given set of numbers.

• The factors are multiplied together to obtain the respective multiples.

• The factors are that integer which when divides the concerned number yields no remainder in the division.

So, we have learnt that there are a total of 9 factors of 36 given by 1,2,3,4,6,9,12, 18, and 36.