Factors of 30 are the list of integers that can be evenly divided into 30. There are 8 factors of 30 in all. In this lesson, we will find the factors of 30, its prime factors, and its factors in pairs. We will also go through some solved examples to understand this topic better.

**Factors of 30:**1, 2, 3, 5, 6, 10, 15, 30**Factors of -30:**-1, -2, -3, -5, -6, -10, -15, -30**Prime Factorization of 30:**2 × 3 × 5

**Table of Contents**

- What are Factors of 30?
- How to Calculate Factors of 30?
- Factors of 30 by Prime Factorization
- Factors of 30 in Pairs
- Important Notes
- FAQs on Factors of 30
- Factors of 30 Solved Examples
- Interactive Questions

## What are Factors of 30?

The factors of 30 are all the integers that 30 can be divided into. The number 30 is an even composite number. A number is said to be composite if it has more than two factors. Since it is even, it will have 2 as a factor. Thus, by understanding the properties of the number 30, we can find the factors of 30 which are 1, 2, 3, 5, 6, 10, 15, and 30.

**Explore factors using illustrations and interactive examples:**

- Factors of 360: The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360.
- Factors of 24: The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
- Factors of 6: The factors of 6 are 1, 2, 3, and 6.
- Factors of 180: The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
- Factors of 45: The factors of 45 are 1, 3, 5, 9, 15, and 45.

## How To Calculate Factors of 30?

**Step 1:**Let's begin calculating the factors of 30 with the idea that any number that completely divides 30 without any remainder is its factor.**Step 2:**Let's start with the whole number 1. We know that 30 ÷ 1 = 30**Step 3:**The next whole number is 2. Now, divide 30 by 2. Thus, 30 ÷ 2 = 15.**Step 4:**Proceeding in this manner we get, 30 ÷ 3 = 10 and 30 ÷ 5 = 6. In this way, we can obtain all the factors of 30.**Step 5:**All these numbers when multiplied make up the factors of 30. That is 30 = 1 × 30, 2 × 15, 3 × 10 and 5 × 6.

## Factors of 30 by Prime Factorization

Prime factorization is to express a composite number as the product of its prime factors.

**Step 1:**To get the prime factors of 30, we divide it by its smallest prime factor, which is 2. Thus, 30 ÷ 2 = 15.**Step 2:**Now, 15 is divided by its smallest prime factor and the quotient is obtained. We get 15 ÷ 3 = 5**Step 3:**This process goes on until we get the quotient as 1.

The prime factorization of 30 is shown below:

## Factors of 30 in Pairs

The pair of numbers that give 30 when multiplied is known as the factor pairs of 30. Following are the factors of 30 in pairs. Since 30 is positive, we have -ve × -ve = +ve.

Product form of 30 |
Pair factor |

1 × 30 = 30 | (1,30) |

2 × 15= 30 | (2,15) |

3 × 10 = 30 | (3,10) |

5 × 6 = 30 | (5,6) |

-1 × -30 = 30 | (-1,-30) |

-2 × -15 = 30 | (-2,-15) |

-3 × -10 = 30 | (-3,-10) |

-5 × -6 = 30 | (-5,-6) |

**Important Notes**

- As 30 ends with the digit 0, it will have 5 and 10 as its factors. This holds true for all numbers that end with the digit 0.
- 30 is a non-perfect square number. Thus, it will have an even number of factors. This property holds true for every non-perfect square number.

## FAQs on Factors of 30

### What are the Common Factors of 24 and 30?

Since, the **Factors of 24** are 1, 2, 3, 4, 6, 8, 12, 24 and the **factors of 30 **are 1, 2, 3, 5, 6, 10, 15, 30. Therefore, the common factors of 24 and 30 are 1, 2, 3, and 6.

### Is 30 a Factor or a Multiple of 10?

30 = 3 × 10. Thus, 30 is a multiple of 10.

### What are the Common Factors of 18 and 30?

**Factors of 18** = 1, 2, 3, 6, 9, 18 and the **Factors of 30 **= 1, 2, 3, 5, 6, 10, 15, 30. Therefore, the common factors of 18 and 30 are 1, 2, 3, and 6.

### What are Prime Factors of 30?

The prime factors of 30 are 2, 3, and 5.

### How to Find Prime Factors of 30?

The prime factors are calculated by the prime factorization of 30 either by division method or by the factor tree method.

## Factors of 30 Solved Examples

**Example 1: **Peter and Andrew both have rectangular papers with dimensions as shown below.

They place the two rectangles one over the other. Since the two shapes do not overlap, Peter informs Andrew that they don't have the same area. However, Andrew does not agree with him. Can you find out who is correct?

**Solution:**

Area of a rectangle = length × breadth. For the first rectangle, Area = 6 × 5 = 30 . For the second rectangle, Area = 10 × 3 = 30.

They have equal areas. Therefore, Andrew is correct as the two rectangles have equal areas.

**Example 2: **Jill has (-3) as one of the factors of 30. How will she get the other factor?

**Solution:**

30 = Factor 1 × Factor 2. We have 30 = (-3) × Factor 2, which means that Factor 2 = 30 ÷ (-3) =(-10).

Therefore, the other factor is -10.

## Interactive Questions

**Here are a few activities for you to practice. **

**Select/Type your answer and click the "Check Answer" button to see the result.**