Factors of 117 are the numbers which when multiplied in pairs give the product as 117. These factors can be negative as well. The number 117 is also is an even composite number, which means that it has several factors. In this lesson, we will calculate the factors of 117, prime factors of 117, and factors of 117 in pairs along with solved examples for a better understanding.

**Factors of 117:** 1, 3, 9, 13, 39 and 117

**Prime Factorization of 117: **117 = 3 × 3 × 13.

**Table of Contents**

- What Are the Factors of 117?
- Important Notes
- How to Calculate Factors of 117?
- Factors of 117 by Prime Factorization
- Factors of 117 in Pairs
- FAQs on Factors of 117
- Solved Examples
- Interactive Questions

## What Are Factors of 117?

Factors of 117 will be those numbers that exactly divide it and give a remainder as 0. This means that the two whole numbers whose product is 117 are the factors of 117. For example, you can get 117 as an answer as:

- 1×117=117
- 9×13=117
- 13×9=117
- 3×39=117
- 117×1=117

## How to Calculate Factors of 117?

Let's begin calculating the factors of 117, starting with the smallest whole number i.e. 1. On dividing 117 with this number, do we get the remainder 0?

Yes! So, we will get

- 117÷1=117
- 117×1=117

Since 117 is an odd number, 2 cannot be a factor. The next whole number to be checked is 3

Now divide 117 with this number.

117÷3 = 39 ⇒ 3 × 39 = 117

Proceeding in a similar manner we get,

117 = 1×117 = 3 × 39 = 9 × 13

Hence, the **factors of 117 are 1, 3, 9, 13, 39 and 117****.**

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

- Factors of 25 - The factors of 17 are 1, 17.
- Factors of 125 - The factors of 125 are 1, 5, 25, and 125
- Factors of 250 - The factors of 250 are 1, 2, 5, 10, 25, 50, 125, 250
- Factors of 110 - The factors of 110 are 1, 2, 5, 11, 22, 55, 110
- Factors of 112 - The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.

**Important Notes**

- While finding factors of any number, we consider only whole numbers and integers.
- Decimal numbers and fractions are not considered as factors of a number.
- All even number definitely have 2 as its factor.

## Factors of 117 by Prime Factorization

"Prime factorization means to express a composite number as the product of its prime factors". To get the prime factorization of 117, we divide it by its smallest prime factor which is 2 then 3, 5 so on and factor and the quotient are obtained. This process goes on till we get the quotient as 1

The prime factorization of 117 is shown below:

A factor tree shows all the factors of a given number and all the factors of the other composite factors of the original number. Have a look at the factor tree of 117 here.

## Factors of 117 in Pairs

The pair of numbers which gives 117 when multiplied are known as factor pairs of 117 Following are the factors of 117 in pairs.

Product form of 117 |
Pair factor |

1 × 117 = 117 | (1, 117) |

3 × 39 = 39 × 3 = 117 | (3, 39) |

9 × 13 = 13 × 9 = 117 | (9, 13) |

Observe in the table above, after 9 × 13, the factors start repeating accept the order. So, it is enough to find factors till (9,13). If we consider negative integers, then both the numbers in the pair factors will be negative.

117 is positive and as we know - ve × - ve = +ve.

## FAQs on Factors of 117

### 1. What number can go into 117?

The numbers that can go into 117 (also called factors of 117) are 1, 3, 9, 13, 39, and 117 itself.

### 2. What is the Highest common factor of 117 and 118?

The only common factor of 117 and 118 is 1. therefore HCF is 1.

### 3. What are all the factors of 117?

Factors of 117 are 1, 3, 9, 13, 39, and 117.

### 4. Is 117 prime or composite?

Factors of 117 are having more than two factors, we will call it a composite number.

## Solved Examples on Factors of 117

**Example 1: **Peter and Andrew both have rectangular rooms carpets with dimensions 13 × 9 inches and 39 × 3 inches.** **They place the two carpets one over others. As both the carpets do not overlap, Peter said that they don't have the same area. However, Andrew does not agree with him.

Can you find out who is correct?

**Solution:**

As we know, Area of a rectangle = length × breadth

Area of the first carpet is 13 × 9 = 117

Area of the second carpet is 9 × 13 = 117

Hence, the two carpets have equal areas. This proves that Andrew was correct.

**Example 2: **Robert's teacher told him that -3 is one of the factors of 117. Can you help him find the other factor?

**Solution:**

117 = Factor 1 × Factor 2

∴117 = (−3) × Factor 2

Factor 2 = 117 ÷ (−3) = (−39)

The other factor is -39.

## 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.**