**factors of 30** are the numbers, which give the result of 30 when multiplied in pairs of two. We can also say that the factors are the numbers that divide a number completely, leaving zero as a remainder. factors of 30 can be positive or negative, but cannot be a decimal or fraction. for example, the factor of 30 can be (1, 30) or (-1, -30). If we multiply the pair of negative numbers, such as multiplying -1 and -30, it will result in an original number 30. In this article, we are going to learn the pair factors and prime factors of 30 using the division method and the method of decomposition into prime factors.

**index:**

Reading: What is all the factors of 30

- what are the factors of 30?
- pair of factors of 30
- find factors of 30 by division
- decomposition on prime factors of 30
- examples
- frequently asked questions

Contents

## what are the factors of 30?

The factors of 30 are the numbers that divide 30 exactly without leaving a remainder. Since the number 30 is an even composite number, it has factors other than 1 and 30. Thus, the factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

## factors of pairs of 30

A pair of numbers, which are multiplied together and result in an original number 30, is called a factor pair of 30. As mentioned above, factor pairs of 30 can be positive or negative. factors of positive and negative pairs of 30 are given below.

**factors of positive pairs of 30:**

**negative factor pair of 30: **

so the positive torque factors of 30 are (1, 30), (2, 15), (3, 10), and (5, 6) and the negative torque factors of 30 are (-1 , -30) , (-2, -15), (-3, -10) and (-5, -6).

## factors of 30 by division method

In the division method, the factors of 30 can be found by dividing the number 30 by different whole numbers. If the whole number divides 30 exactly, then those whole numbers are the factors of 30. Now, let’s discuss how to find the factors of 30 using the division method.

Now, let’s start by dividing 30 by 1, and then move on to consecutive integers.

- 30/1 = 30 (factor = 1 and remainder = 0)
- 30/2 = 15 (factor = 2 and remainder = 0)
- 30/ 3 = 10 (factor = 3 and remainder = 0)
- 30/5 = 6 (factor = 5 and remainder = 0)
- 30/6 = 5 (factor = 6 and remainder = 0)
- 30/10 = 3 (factor = 10 and remainder = 0)
- 30/15 = 2 (factor = 15 and remainder = 0)
- 30/30 = 1 (factor = 30 and remainder = 0)

If you divide 30 by any number other than 1, 2, 3, 5, 6, 10, 15, and 30, you are left with a remainder. therefore, the factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

**also, read**:

## prime factorization of 30

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The number 30 is a composite number. now let’s find the prime factors of it.

- The first step is to divide the number 30 by the smallest prime number, i.e. 2.

30 ÷ 2 = 15

- again, divide 15 by 2.

15 ÷ 2 = 7.5; the factor cannot be a fraction.

- now, proceed to the next prime number i.e. 3 and divide 15 with it.

15 ÷ 3 = 5

- again, if we divide 5 by 3, we get a fractional number, which we can’t consider as a factor.
- therefore, we will go to the next prime number, which is 5 .

5 ÷ 5 = 1

- we have received 1 at the end and furthermore, we cannot continue with the division method. then, the
**prime factorization of 30 is 2 × 3 × 5**, where 2, 3 and 5 are the prime numbers.

## video lesson on prime factors

### examples

**example 1:**

find the common factors of 30 and 31.

**solution:**

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

the divisors of 31 are 1 and 31.

so the common factor of 30 and 31 is just 1, since 31 is a prime number.

**example 2:**

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find the common factors of 30 and 29.

**solution:**

factors of 30 = 1, 2, 3, 5, 6, 10, 15 and 30.

factors of 29 = 1 and 29.

therefore, the common factor of 30 and 29 is 1.

**example 3:**

find the common factors of 30 and 15.

**solution:**

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

The factors of 15 are 1, 3, 5, and 15.

therefore, the common factors of 30 and 15 are 1, 3, 5 and 15.

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