What are Factors?
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 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.
Positive Factors of 30 are | 1, 2, 3, 5, 6, 10, 15, 30. |
Negative Factors of 30 are | -1, -2, -3, -5, -6, -10, -15,-30 |
Hence 30 have total 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 UploadedSoon].
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)
2 | 120 |
2 | 60 |
2 | 30 |
3 | 15 |
5 | 5 |
1 |
2 | 360 |
2 | 180 |
2 | 90 |
5 | 45 |
3 | 9 |
3 | 3 |
1 |
2 | 428 |
2 | 214 |
17 | 17 |
1 |
2 | 84 |
2 | 42 |
3 | 21 |
7 | 7 |
1 |
2 | 12 |
2 | 6 |
3 | 3 |
1 |
vi) Factors of 70 are:
2 | 70 |
5 | 35 |
7 | 7 |
1 |
2 | 66 |
3 | 33 |
11 | 11 |
1 |
Q1. What is the Difference Between Factors and Prime Factors and What is the Difference Between a Factor and a Multiple?
Ans. Factor is a number that can be further broken down. It is all the number 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 to 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.
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