Factors

# Factors of 135 | Prime Factorization of 135 | Factor Tree of 135

Written by Prerit Jain

Updated on: 15 Feb 2023

Contents

### Factors of 135 | Prime Factorization of 135 | Factor Tree of 135

## Factors of 135

Factors of 135 | Factor Pairs of 135 | Prime factors of 135 |

1, 3, 5, 9, 15, 27, 45 and 135. | (1, 135), (3, 45), (5, 27), and (9, 15) | 3 × 3 × 3 × 5 |

Calculate Factors of

**The Factors are**

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## What are the factors of 135

To find the factors of 135, we can first list all numbers from 1 to 135 in ascending order. Then, take each number and divide it into 135 – if there’s no remainder left after division then that is a factor! We found out some fascinating facts about this number: The factors are 1, 3, 5, 9,15, and 45 and135 which make up its ‘factoring family’ for adding together to equal the original product – which would be what you get when multiplying them together again (e.g., 45 x 3 = 135). Pretty cool stuff indeed!

## How to Find Factors of 135

The various methods through which you can find the factors of a number are given below and they can also be used to find the factors of 135.

- Factor of 124 using Multiplication Method
- Factors of 124 using Division Method
- Prime Factorization of 124
- Factor tree of 124

## Factors of 135 using Multiplication Method

Factors are the numbers that multiply together to form a certain number – like two parents who come together to make a baby! To find out which factors belong with 135, we can use the multiplication method. All you have to do is take 1 and it’s friend (135) and join them up in pairs; then just multiple both of them together until each pair makes 135. That way, you’ll discover that those same two friends —1 & 135—are actually its only set of factors!

Factors of 135 Using Division Method

To find the prime factors of 135, we can use a process called division. First, divide 135 by the smallest prime number that is less than or equal to its square root (in this case 3). When you do this calculation, you will get 45 with no remainder which means 3 is one factor of your number! Now repeat it for 45 and see what other numbers remain as factors! By doing so until there are only 2 remaining numbers left in our equation- these two would be considered “prime” because they cannot be further divided -we have found all those special individual denominators known as Prime Factors.

## Prime Factorization of 135

Calculate Prime Factors of

The Prime Factors of 135 =

3 x

3 x

3 x

5

To understand the prime factorization of a number, let’s take 135 as an example. The steps would be to start by dividing it by the smallest possible prime number, which is 2 in this case. Since that result wasn’t divisible evenly into an integer value we go on and find the next smallest prime number – 3! When divided by 3 consecutively three times (3 x 3 x 3), you get 5 at last; since being a ‘prime’ itself, we can incorporate this within our answer for ‘135’ – thus resulting in its Prime Factorization: “3 X 3 X 3 x 5.

## Factor tree of 135

To understand how factor trees work, let’s look at an example. For the number 135,

- we can identify its prime factors by breaking them down into smaller numbers until there are no more divisors that produce a whole number answer.
- First, we divide it by 3 – since 3 is one of the smallest prime numbers- to get 45; then using 5 as our next divisor (since it is also a small prime), we end up with 9 and 1 respectively as other components of 135’s original equation!
- In conclusion, when trying to find all of the different combinations in which you can combine these three separate pieces together (3x5x9) they will equal back out to give us our starting point: 135!

## Factor Pairs of 135

Calculate Pair Factors of

1 x 135=135

3 x 45=135

5 x 27=135

9 x 15=135

15 x 9=135

27 x 5=135

45 x 3=135

So Pair Factors of 135 are

(1,135)

(3,45)

(5,27)

(9,15)

(15,9)

(27,5)

(45,3)

To understand how factor trees work, let’s look at an example.

- For the number 135, we can identify its prime factors by breaking them down into smaller numbers until there are no more divisors that produce a whole number answer.
- First, we divide it by 3 – since 3 is one of the smallest prime numbers- to get 45; then using 5 as our next divisor (since it is also a small prime), we end up with 9 and 1 respectively as other components of 135’s original equation!
- In conclusion, when trying to find all of the different combinations in which you can combine these three separate pieces together (3x5x9) they will equal back out to give us our starting point: 135!

## Factors of 135 – Quick Recap

**Factors of 135:** 1, 3, 5, 9, 15, 27, 45, and 135.

**Negative Factors of 135:** -1, -3, -5, -9, -15, -27, -45, and -135.

**Prime Factors of 135: **3 × 3 × 3 × 5

**Prime Factorization of 135:** ** **3 × 3 × 3 × 5

## Fun Facts of Factors of 135

135 is an intriguing number!

It has more than two factors, which means it’s not a prime number. Instead of being called composite numbers though, some people like to call them “positively plentiful” because they have so many positive factors – in the case of 135 that would be 1, 3, 5 9 15 27 45, and even 135 itself! This makes it the smallest known quantity with eight different positive values.

## Examples of Factor of 135

**1. There are 135 students in the school. If there are 9 desks per classroom, how many classrooms do they need? **

**Answer: **15 classrooms (135 / 9 = 15).

**2. Carl has 135 coins consisting of dimes and quarters in his piggy bank. If he has 4 times as many dimes as quarters, how many quarters does he have? **

**Answer:** 45 quarters (4 x 45 = 180; 180 – 135 = 45).

**3. John wants to divide his 135 jellybeans evenly among his friends without any leftovers. How many can each friend get if there are 8 friends altogether? **

**Answer:** 17 jellybeans (135 / 8 = 16 7/8; round up to 17).

**4. A bakery buys 135 packs of flour for $10 each, 3 cents more than the original price per pack. What was the original price of one pack of flour? **

**Answer: **7 cents ((10 – 3) / 135 = 0.05).

**5. Caroline needs to cut a piece of fabric that is 135 feet long into smaller pieces that are 5 feet long each for a project at school. How many 5-foot pieces can she cut from the fabric? **

**Answer: **27 pieces (135 ÷ 5 = 27).

**6. Thomas has a lemon tree with 135 lemons on it and he collects all the lemons one by one every day starting with Monday until Saturday when the tree is empty again. How many lemons does Thomas collect on Tuesday? **

**Answer:** 35 lemons (135 – 100 = 35).

**7 .If someone buys 150 apples for $14,1 cents more than each apple costs, what was the cost for one apple? **Answer : 13 cents ((14-1)/150= 0 .09 ).

**8. A family reunion consists of 15 people so every family brings 8 food items. How many food items do they bring altogether?**

Answer: 120 food items (15×8=120 )

**9. Is 72 a factor of 135?**

**Answer:**Yes, 72 is a factor of 135 (135÷72=1 with the remainder 63 ).

**10. If someone jogs 11 laps around an oval track that measures 131 meters, how far have they run?**

Answer:1441 meters (131×11=1441 ).

Answer:

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## Frequently Asked Questions on Factors of 135

**What are the factors of 135?**

The factors of 135 are 1, 3, 5, 9, 15, 27, 45, and 135.

**How do you find the factors of 135? **

To find the factor of a number, simply divide the number by each number between 1 and itself until you cannot go any further without getting a decimal or fractional answer.

**How many factors does 135 have?**

There are eight factors for 135: 1, 3, 5, 9, 15, 27, 45, and 135.

**What is the prime factorization of 135?**

The prime factorization of 135 is 3 x 3 x 5 x 5.

**What is a factor tree for 135?**

A Factor Tree for 135 would look like this:

135 / \ 3 45 / \ / \ 5 9 15 27 / \ / \ 1 3 5 9

**Is 36 a factor of 135? **

Yes, 36 is a factor of 135 (135 ÷ 36 = 3).

**Is 70 a factor of 135?**

No, 70 is not a factor of 135 (135÷70=1 with the remainder of 65 ).

**if someone buys 140 apples for $ 12,2 cents more than each apple costs,what was the cost for one apple?**

10 cents ((12-2)/140= 0 .08 ).

**A family reunion consists of 14 people so every family brings 11 food items. How many food items do they bring altogether? **

154 food items (14×11=154 )

**If someone jogs 13 laps around an oval track which measures 134 meters, how far have they run?**

1722 meters (134×13=1722 )

Written by by

Prerit Jain