Factors

# Factors of 117 | Prime Factorization of 117 | Factor Tree of 117

Written by Prerit Jain

Updated on: 15 Feb 2023

Contents

### Factors of 117 | Prime Factorization of 117 | Factor Tree of 117

## Factors of 117

Factors of 117 | Factor Pairs of 117 | Prime factors of 117 |

1, 3, 9, 13, 39, 117 | (1, 117), (3, 39), (9, 13) | 3 × 13 |

Calculate Factors of

**The Factors are**

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## What are the factors of 117

A factor of a number is a number that can divide the given number evenly without any decimal points in the quotient and with zero remainders. So, for example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because all of those numbers can evenly divide the number 12.

To find the factors of 117, we can start by dividing 117 by 2. If 117 is evenly divisible by 2, then 2 is a factor of 117. If 117 is not evenly divisible by 2, then we can try dividing it by 3, and so on.

Here’s how it would work:

- 117 / 2 = 58.5 (not evenly divisible)
- 117 / 3 = 39 (not evenly divisible)
- 117 / 4 = 29.25 (not evenly divisible)
- 117 / 5 = 23.4 (not evenly divisible)

We can keep going like this until we find a number that 117 is evenly divisible by a number. But if we keep going, we will eventually find that 117 is evenly divisible by 1 and 117. So, the factors of 117 are 1 and 117.

## How to Find Factors of 117

The most prominent methods of finding the factors of a number are as given below and they can be used to find the factors of 117 also.

- Factor of 117 using Multiplication Method
- Factors of 117 using Division Method
- Prime Factorization of 117
- Factor tree of 117

## Factors of 117 using Multiplication Method

To find the factors of 117 using the multiplication method, we can create a list of pairs of numbers whose product is 117. The factors of 117 will be the numbers in each pair.

For example, here are all the pairs of numbers whose product is 117:

1 x 117 = 117

3 x 39 = 117

9 x 13 = 117

So, the factors of 117 are 1, 3, 9, 13, and 117.

## Factors of 117 Using Division Method

To find the factors of 117 using the division method, we can start by dividing 117 by 2. If 117 is evenly divisible by 2, then 2 is a factor of 117. If 117 is not evenly divisible by 2, then we can try dividing it by 3, and so on.

Here’s how it would work:

- 117 / 2 = 58.5 (not evenly divisible)
- 117 / 3 = 39 (not evenly divisible)
- 117 / 4 = 29.25 (not evenly divisible)
- 117 / 5 = 23.4 (not evenly divisible)

We can keep going like this until we find a number that 117 is evenly divisible by. But if we keep going, we will eventually find that 117 is evenly divisible by 1 and 117. So, the factors of 117 are 1 and 117.

## Prime Factorization of 117

Calculate Prime Factors of

The Prime Factors of 117 =

3 x

3 x

13

In prime factorization, we try to express a number as a product of its prime factors. A prime number is a number that is only divisible by 1 and itself. For example, the first few prime numbers are 2, 3, 5, 7, 11, and 13.

To find the prime factorization of 117, we can start by dividing 117 by the smallest prime number, which is 2. If 117 is evenly divisible by 2, then we can divide it by 2 again and again until we get a number that is not evenly divisible by 2.

Here’s how it would work:

- 117 / 2 = 58.5 (not evenly divisible). Since 117 is not evenly divisible by 2, we move on to the next smallest prime number, which is 3.
- 117 / 3 = 39 (not evenly divisible). Again, 117 is not evenly divisible by 3, so we move on to the next smallest prime number, which is 5.
- 117 / 5 = 23.4 (not evenly divisible). Since 117 is not evenly divisible by 5, we move on to the next smallest prime number, which is 7.
- 117 / 7 = 16.7 (not evenly divisible). Since 117 is not evenly divisible by 7, we move on to the next smallest prime number, which is 11.
- 117 / 11 = 10.63 (not evenly divisible). Since 117 is not evenly divisible by 11, we move on to the next smallest prime number, which is 13.
- 117 / 13 = 9 (evenly divisible). Since 117 is evenly divisible by 13, we can divide 117 by 13 again to get 9.
- 9 / 13 = 0.69 (not evenly divisible). Since 9 is not evenly divisible by 13, we are done.

Therefore, the prime factorization of 117 is 13 x 9, or 13 x 3^2. This means that the prime factors of 117 are 13 and 3, and 3 appears twice in the prime factorization.

## Factor tree of 117

To create a factor tree for 117, we can start by finding two factors of 117 whose product is 117. For example, we can find that 9 and 13 are both factors of 117 because 9 x 13 = 117.

Next, we can find two factors of 9 whose product is 9. For example, we can find that 3 and 3 are both factors of 9 because 3 x 3 = 9.

Finally, we can create a tree-like diagram to represent the factors of 117. It would look like this:

## Factor Pairs of 117

Calculate Pair Factors of

1 x 117=117

3 x 39=117

9 x 13=117

13 x 9=117

39 x 3=117

So Pair Factors of 117 are

(1,117)

(3,39)

(9,13)

(13,9)

(39,3)

The factor pairs of 117 are all the pairs of numbers that can be multiplied together to equal 117. For example, the factors pairs of 117 are (1, 117), (3, 39), and (9, 13).

We can find all the factor pairs of 117 by dividing 117 by every number between 1 and 117. If 117 is evenly divisible by a number, then that number and 117 divided by that number are both factors of 117.

For example, if we divide 117 by 2, we get 58.5, which is not a whole number. So, 2 is not a factor of 117. If we divide 117 by 3, we get 39, which is also not a whole number. So, 3 is not a factor of 117.

We can keep going like this until we find all the factor pairs of 117. In total, there are 3 factor pairs of 117: (1, 117), (3, 39), and (9, 13).

## Factors of 117 – Quick Recap

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

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

**Prime Factors of 117:** 3 × 1 3

**Prime Factorization of 117:** ** ** 3 × 1 3

## Fun Facts of Factors of 117

- The factor pairs of 117 are all the pairs of numbers that can be multiplied together to equal 117. For example, the factors pairs of 117 are (1, 117), (3, 39), and (9, 13).
- We can find all the factor pairs of 117 by dividing 117 by every number between 1 and 117. If 117 is evenly divisible by a number, then that number and 117 divided by that number are both factors of 117.
- For example, we can divide 117 by 2 to see if it is a factor of 117. If we divide 117 by 2, we get 58.5, which is not a whole number. So, 2 is not a factor of 117. We can then divide 117 by 3 to see if it is a factor of 117. If we divide 117 by 3, we get 39, which is also not a whole number. So, 3 is not a factor of 117.
- We can keep going like this until we find all the factor pairs of 117. In total, there are 3 factor pairs of 117: (1, 117), (3, 39), and (9, 13).

## Examples of Factor of 117

**1. If a box contains 117 apples, how many apples would each person get if the box was split evenly among three people?**

**Answer: **Each person would get 39 apples.

**2. Joe needs to divide his collection of 117 marbles into three equal piles, how many marbles will be in each pile? **

**Answer:** 39 marbles in each pile.

**3. A store has 117 candy bars for sale, and there are 4 customers who want to buy them. How many candy bars does each customer get? **

**Answer:** Each customer gets 29 candy bars.

**4. Maria has 117 pages of notes to study, and she wants to allocate the same amount of time for studying each page. How much time should Maria spend on one page? **

**Answer:** Maria should spend 1 minute on each page.

**5. Harry is baking a cake with 117 ingredients, and he wants to know how many ingredients should be added in each bowl of the cake mixture. How many ingredients should Harry add to each bowl? **

**Answer: **Harry should add 39 ingredients per bowl of cake mixture.

**6. Scott has an assignment due with a total word count of 1197 words, and he needs to divide it into 5 sections equally with the same number of words in each section, what is the word count per section that Scott requires? **

**Answer: **Each section should have 239 words.

**7 What is the greatest common factor between two numbers where one number equals 1177 and the other equals 1208? **

**Answer:** The greatest common factor between 1177 and 1208 is 39.

**8 What is the lowest common multiple between 1177 and 1208? **

**Answer: **The Lowest Common Multiple (LCM) between 1177 and 1208 is 450072 .

**9 Anne baked a batch of cookies containing 117 pieces, she wants 3 children at her party to share them equally, how Many cookies does Anne need to give To Each Child? **

**Answer: **Anne needs to give 39 cookies per child.

1**0 Amanda found out that her number 1197 can be factored into four different prime numbers – 1, 3 ,39 , and 117 – to determine which two prime numbers when multiplied together will equal 1197. **

**Answer:** Multiplying 1 and 117 together yields 1197.

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## Frequently Asked Questions on Factors of 117

**What are the factors of 117?**

The factors of 117 are 1, 3, 39, and 117.

**How many factors does 117 have?**

117 has 4 factors; 1, 3, 39, and 117.

**Is 117 a prime number? **

No, 117 is not a prime number since it has more than two distinct factors.

**What are the common factors of 117?**

The common factors of 117 are 1 and 3.

**Is one a factor of 117?**

Yes, one is a factor of 117 since any number divided by one will result in that same exact number (117).

**How do you find the factors of 117?**

You can find the factors of 117 by first listing out all its divisors starting with one and ending at itself (117). Then check each divisor to see if it divides into other numbers or not (For example; checking if 3 divides into 39 or not). Once you’ve checked all numbers you’ll know the exact amount and value of each factor for that particular number (117).

**Are there any negative factors for the number 117?**

No, there are no negative factors for the number 117 as any factor multiplied by a negative will result in a negative value which cannot be factored from this positive integer (117).

**What is an example of using the greatest common factor to find the GCF for two numbers including 1197?**

To find the greatest common factor between two integers using 1197 as an example; first list out all its divisors starting with one and ending at itself (1197), then repeat this process for your other integer (for example; finding all possible divisors from 1208) then compare these two sets to look for overlaps between them both to determine what’s they’re greatest common factor because those will be shared between them both minus any others which may have been found by either set independently but not as part of their combined pair containing 1197 & 1208 in our example case here today!

**What is an example of using prime factorization to solve 1197?**

To use prime factorization with 1197 as an example; start off by dividing it down until it can’t be divided anymore while keeping track the entire time on paper or digitally whichever works best for you along with writing down which primes were used in process here to minimize overall time spent factoring larger numbers like ours today – once done take those same primes used in order from least to greatest placing them together now as our final product thus having finished our usage correctly!

**Could we divide some other numbers into 1197 besides its own four listed above (1,3,39 & 177)?**

No, none other than these four listed can be divided from within this specific number here today due to it being composite so even attempting to attempt further division would only lead nowhere else further wasting your valuable moments!

Written by

Prerit Jain