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
(Image will be Uploaded Soon)
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.
FAQs on Factors of 30
1. What is the difference between factors and prime factors? What is the difference between a factor and a multiple?
Factor is a number that can be further broken down. It is all the numbers that can be multiplied to give the original number, but a prime factor cannot be broken down.
For example, the factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. But the prime factors of 30 are 2, 3, and 5.
Factors and multiples are very different from each other yet it is very confusing to remember what is what?!! Well, let us clarify it now, a factor is an exact divisor of a number whereas a multiple is the result we get after the multiplication is done.
2. Write down all the factors of the 30 in each category like prime factors. Also, give the sum of all the main factors of 30.
Factors of 30, are numbers which when multiplied in pairs can give the resultant product equally to 30. There is an overall total of 8 factors of 30. These factors can either be positive integers or negative.
The list of all the positive integer factors of 30 is 1, 2, 3, 5, 6, 10, 15, and 30.
List of all the negative integer factors of 30 are -1, -2, -3, -5, -6, -10, -15 and -30.
Prime factors of the number 30 are 2, 3, and 5.
Now to calculate the sum of all the positive values of the factors of the number 30:
Sum = 1 + 2 + 3 + 5 + 6 + 10 + 15 + 30 = 72
3. What are the important notes about the factors of 30?
Let us talk about some of the important notes or points to remember by the factorisation of the number 30.
The number 30 ends with the digit 0 and having the last digit as zero means the number must have 5 and 10 as its factors, thus the number 30 will also have 5 and 10 as its factors.
30 is not a perfect square number. Thus, it will have an even number of integers. This is a property of all the non-perfect square numbers.
There are around 8 positive factors and positive pairs of the factors of the number 30.
4. What is meant by Factorisation and factors?
Factorisation of a number like 30, means to break that number or entity into a product of another number (factor) or entity, which can be again multiplied to get the original number or entity. The primary goal of factorisation is to reduce any equation or number into a simpler form with the help of factors, so it can be easier to do calculations.
The factors of any number or equation can be simple numbers, a variable, or an algebraic expression itself. The factor will always be either smaller or at best equal to the original number.