**Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30**.

Here is complete detailed methods to find the factors of 30.

Actually, Factor is a number which divides any number completely without leaving remainder.

Or simply we can say that if we multiply two whole numbers (positive & negative) and it gives a product. Then the numbers that we multiply, are the factors of the product.

For example, if we multiply 5 to 6, it gives 30. Here 5 and 6 are called positive factors and if we multiply -3 to -10, it gives 30. So -3 and -10 are called negative factors.

Table of Contents

## How to Find The Factors of 30 ?

Since factors of 30 are the numbers, which divides 30 completely without leaving remainder. So here we are going to divide 30 by all numbers up to 30. Let’s see the process –

We have to stop the process, if any number of column ‘B’ appears in column ‘A’ or when any element comes in both columns at same level and this element will consider as a factor.

Here we stop the division when 6 appears in column ‘A’, which has already been came in column ‘B’.

Hence, all the factor of 30 in above table are : 1 ,2, 3, 5, 6, 10, 15, 30

Similarly, negative factor of 30 are : -1, -2, -3, -5, -6, -10, -15, -30

## What Are The Factors of 30 in Pairs ?

As we saw in above table, 3 multiply by 10 gives 30. So (3, 10) is a factor pair of 30. Let us see how many factor pairs can be achieved –

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

30 x 1 = 30

Similarly, negative factor pairs of 30 can be written as follows –

-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

-30 x -1 = 30

Hence, 30 has 8 factor pairs.

## What Are the Prime Factors of 30 ?

The **Prime Factors of 30 **are **2, 3 & 5**. Here we will discuss, mainly two methods of factorization to find Prime Factors of any number.

- Division Method
- Factor Tree Method

### Prime Factors of 30 by Division Method

**Step 1 :** Divide the number by the smallest prime number, which divides the number exactly.**Step 2 :** Divide the quotient again by the smallest prime number. If quotient is not exactly divisible by the

smallest prime number, choose next smallest prime number.**Step 3 :** Repeat Step 2 again and again till the quotient becomes 1.**Step 5 :** All the prime numbers used in above process are the prime factors.

Check : Multiply all the prime factors, the multiplication should be the number itself.

Caution : In this method, only prime numbers will be use to divide.

- First of all, we divide 30 by smallest prime number i.e. 2. we got 15 as quotient and remainder is zero. (Note – if remainder will not zero, means doesn’t divide exactly, try next prime number to divide)
- Again we divide 15 by smallest prime number i.e. 2, we didn’t get a whole number as quotient. So try next prime number i.e. 3. We got 5 as quotient.
- Since 5 is a prime number, so 5 will divide by itself only.
- Here we divide 5 by 5 and we got 1 as a quotient.

Hence, 30 = 2 x 3 x 5

So **30 has two prime factor i.e. 2, 3 & 5.**

### Factor Tree of 30

**Step 1 :** Write a number as root of the tree**Step 2 :** Find the factors of the number, each factor will be considered as root again (now, we got 2 new root)**Step 3 :** Repeat step 2 until we can’t factor any more (or until we got prime factor)**Step 5 :** The end nodes are the prime factors.

We can initiate the tree by choosing any two factors. Here we choose 2 and 15 as factors of 30. Further 15 will split into 3 and 5.

We got the same unique nodes in every tree.

The Factor Tree may be made so many types depends upon choosing the initial and middle factors.

## Number of Factors of 30

The **Number of Factors of 30 is 8**. To find the number of factors, we use Division Method.

In our example, as we saw above 30 = 2 x 3 x 5.

**Number of factors is = (power + 1)(power + 1)(power + 1)………. **

Hence number of **factors of** **30 **is = (1 + 1)(1 + 1)(1 + 1)= 2 x 2 x 2 = 8

and if we consider both positive and negative factors, then

total no. of factors = 8 (positive) + 8 (negative) = 16

I hope, this step-by-step tutorial will be helpful to understand factorization method of 30.

## FAQ

### What are the factors or divisors of the number 30?

The factors or divisors of the number 30 are 1, 2, 3, 5, 6, 10, 15, 30.

### What are the prime factors of the number 30?

The prime factors of the number 30 are 2, 3 & 5.

### What is the total number of factors of the number 30?

The total number of factors of the number 30 is 10.

### What is the total number of prime factors of the number 30?

The total number of prime factors of the number 30 is 3.

### What is the sum of all factors of the number 30 including 30?

The sum of all the factors of the number 30 including 30 is 72 (i.e 1 + 2 + 3 + 5 + 6 + 10 + 15 + 30 = 72)

### What is the sum of all factors of the number 30 excluding 30?

The sum of all the factors of the number 30 excluding 30 is 42 (i.e 1 + 2 + 3 + 5 + 6 + 10 + 15 = 42)

### What are the factor combinations of the number 30?

The factor combinations of the number 30 are (1, 30) , (2, 15) , (3, 10), (5, 6), (6, 5), (10, 3), (15, 2) & (30, 1).

### What is the prime factorization of the number 30?

The prime factorization of the number 30 are 2, 3 & 5.

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