[Maths Class Notes] on Factors of 30 Pdf for Exam

Factors of a number are the product of such numbers which completely divide the given number. Factors of a given number can be either positive or negative numbers. By multiplying the factors of a number we get the given number. For example 1, 2, 4, 8 are the factors of 8. On multiplying two or more numbers we get 8. Hence we have 4 x 2 = 8 or 1 x 8 = 8. In this article, we will study all the factors of 30 definitions and also how to find all the factors of 30 and the factor tree of 30.

Note: The numbers we multiply are the factors and the resultant is called a product.  

Given below is another example of factors and multiples (product).

Factors of 30 Definition

The factors of a number are defined as the numbers which when multiplied will give the original number, by multiplying the two factors we get the result as the original number. The factors can be either positive or negative integers.

Factors of 30 are all the integers that can evenly divide the given number 30.

Now let us find all factors of 30.

How to Find the Factors of 30 and What are the factors of 30?

According to the definition of factors of 30 we know that factors of 30 are all the positive or negative integers which divide the number 30 completely. So let us simply divide the number 30 by every number which completely divides 30 in ascending order till 30.

30 ÷ 1 = 30

30 ÷ 2 = 15

30 ÷ 3 = 10

30 ÷ 5 = 6

30 ÷ 6 = 5

30 ÷ 10 = 3

30 ÷ 15 = 2

30 ÷ 30 = 1

So the factors of 30: 1, 2, 3, 5, 6, 10, 15, and 30.

We know that factors also include negative integers hence we can also have, 

list of negative factors of 30 :-1, -2, -3, -5, -6, -10, -15 and -30.

All Factors of 30 can be Listed as Follows.

Hence 30 have a total of 8 positive factors and 8 negative factors.

Factors Pairs of 30

Factor Pairs of 30 are combinations of two factors that when multiplied together give the number 30.

List of all the Positive Factor Pairs of 30

1 x 30 = 30

2 x 15 = 30

3 x 10 = 30

5 x 6 = 30

6 x 5 = 30

10 x 3 = 30

15 x 2 = 30

As we know that Factors of 30 include negative integers too. 

List of all the Negative Factor Pairs of 30:

-1 x -30 = 30

-2 x -15 = 30

-3 x -10 = 30

-5 x -6 = 30

-6 x -5 = 30

-10 x -3 = 30

-15 x- 2 = 30

Prime Factorization of 30 (Prime factors of 30)

According to the prime factor definition we know that the prime factor of a number is the product of all the factors that are prime( a number that divides by itself and only one). Hence we can list the prime factors from the list of factors of 30.

Or the other way to find the prime factorization of 30 is by prime factorization or by factor tree.

How to Calculate Prime Factorization of 30?

To calculate the prime factorization of 30, first, take the least prime number that is 2. Divide it by 2 until it is completely divisible by 2. If at a point it is not divisible by 2 take the next least prime number that is 3. Perform the same steps and move forward, till we get 1, as the quotient. Here is the stepwise method to calculate the prime factors of 30

Step 1: Divide 30 with 2

 30 ÷ 2 = 15

Step 2: Now 15 is no more divisible by 2, move to the next prime number i.e. 3

15 ÷ 3 = 5

Step 3: Now 5 is no more divisible by 3, move to the next prime number i.e. 5

 5÷ 5= 1

Step 4: At last, divide 1 with 1 to get 1.

1 ÷ 1 = 1

From the above steps, we get a prime factor of 30 as 2 × 3 × 5.

And also, Let’s know the factor tree of 30.

Here is the factor tree of 30

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Solved Examples on Factors of 30-

Example 1) find the factors of the following numbers: 

i) 120

ii) 360

iii) 428

iv) 84

v) 12

vi) 70

vii) 66

Solution 1)

i) Factors of 120 are: 

ii) Factors of 360 are:

iii) Factor of 428 are:

iv) Factors of 84 are:

v) Factors of 12 are:

vi) Factors of 70 are:

vii)   Factors of 66 are:

Example 2: Poonam and Anuradha have got rectangular papers with dimensions for one rectangular paper 3 × 10 sq. inches and for the other one 6 × 5 sq. inches. They place the two rectangular papers one over the other to check whether they superimpose or not and since the two shapes do not overlap, Poonam informs Anuradha that they don’t have the same area as they didn’t superimpose. However, Anuradha opposes this idea. How can they find out who is correct, help them?

Solution 2: Area of a rectangular paper = length × breadth. 

For the first rectangular piece of paper, Area = 3 × 10 = 30 sq. inches. And similarly for the second rectangular piece of paper, Area = 6 × 5 = 30 sq. inches.

Hence, therefore, we can say that they both have equal areas. 

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 

Example 3: Jatinder has (-6) as one of the factors of 30. He wants to find the factor that makes the pair of factors of the number 30 with -6. 

Solution 3: We know that 30 = Factor 1 × Factor 2. We have 30 = (-6) × Factor 2

By solving the above equation factor 2 = 30 ÷ (-6) =(-5).

Therefore, the other factor is -5.