# Finding Factors of 280: A Comprehensive Guide

- Author: Noreen Niazi
- Last Updated on: December 15, 2023

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ToggleDo you know what is the factors of 280? How can we calculate it? Which are different methods to calculate the factors of 280? We can find different methods.

Let’s dive into details and discuss in detail about the factors, prime factors, division methods and factors tree to determine the factors of 280.

## Understanding Factors of 280

In mathematics, factors are numbers that divide another number without leaving a remainder. For the number 280, let’s explore the methods to identify its factors.

## Method 1: Trial Division method to find factors of 280

Factors of **280** can be found by checking the divisibility of **280** by the whole numbers 1 through.

$\sqrt{\mathbf{2}\mathbf{8}\mathbf{0}}$≈ 16.73. If a whole number of divides **280** exactly, both

- the number itself and
- the result of the division by that number

are the factors of **280**.

**280**is divisible by**2**. Write**2**to the left. When**280**is divided by**2**the result is**140**. Write**140**under**280****140**is divisible by**2**. Write**2**to the left. When**140**is divided by**2**the result is**70**. Write**70**under**140****70**is divisible by**2**. Write**2**to the left. When**70**is divided by**2**the result is**35**. Write**35**under**70****35**is divisible by**5**. Write**5**to the left. When**35**is divided by**5**the result is**7**. Write**7**under**35****7**is divisible by**7**. Write**7**to the left. When**7**is divided by**7**the result is**1**. Write**1**under**7**

## Method 2: Pair Factors of 280

To begin our investigation, let’s use a simple approach: listing factors in pairs. Suppose you are opening a box and you start with 1 and the number itself, and you gradually open up factors in pairs until you get to the middle. This practical method is similar to finding the ingredients in a recipe with mathematics.

**Pair Factors of 280:**

**280** has **16** factors.

**Factors:**

**1**, **2**, **4**, **5**, **7**, **8**, **10**, **14**, **20**, **28**, **35**, **40**, **56**, **70**, **140**, **280**

**Factor Pairs:**

**1**×**280**=**280****2**×**140**=**280****4**×**70**=**280****5**×**56**=**280****7**×**40**=**280****8**×**35**=**280****10**×**28**=**280****14**×**20**=**280**

## Positive and Negative Factors

**Positive Factors**

1 | 2 | 4 | 5 | 8 | 10 | 14 | 20 | 28 | 35 | 56 | 70 | 140 | 280 |
---|

**Negative Factors**

-1 | -2 | -4 | -5 | -8 | -10 | -14 | -20 | -28 | -35 | -56 | -70 | -140 | -280 |
---|

## Calculating Prime Factors

Prime factors are the building blocks of a number. They are the prime numbers that multiply to give the original number.

**Prime Factors of 280:**

**280** = **2** × **2** × **2** × **5** × **7**

**280** = **2 ^{3}** ×

**5**×

**7**

## Factors Tree

A factors tree is a visual representation of the prime factorization of a number.

## Practice Questions for factors of 280

- If the length of a rectangular garden is 14 meters, what could be the width if the area is 280 square meters?
- A factory produces 280 widgets in a day. If they pack them in boxes of 35 widgets each, how many boxes do they need?
- Bob has 280 marbles. If he wants to distribute them equally among 4 friends, how many marbles will each friend get?
- The sum of two numbers is 280, and their difference is 20. What are the two numbers?
- A rectangular room has an area of 280 square feet. If the length is 20 feet, what is the width?

## FAQs about factors of 280

**Q1: Can a number have more than one set of factors?** Yes, a number can have multiple sets of factors. For example, 12 has factors (1, 12), (2, 6), and (3, 4).

**Q2: What are negative factors?** Negative factors are simply the negations of the positive factors. For instance, -2 is a negative factor of 280 because $-2\times -140=280$.

**Q3: Can decimals be factors?** No, factors are integers. Decimals and fractions are not considered factors.

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