Factors

# Factors of 136 | Prime Factorization of 136 | Factor Tree of 136

Written by Prerit Jain

Updated on: 15 Feb 2023

Contents

### Factors of 136 | Prime Factorization of 136 | Factor Tree of 136

## Factors of 136

Factors of 136 | Factor Pairs of 136 | Prime factors of 136 |

1, 3, 5, 9, 15, 27, 45, and 136. | (1,136) (2,68) (4,34) (8,17) (17,8) (34,4) (68,2) | 2 × 2 × 2 × 17 |

Calculate Factors of

**The Factors are**

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## What are the factors of 136

The factors of a number are the numbers that can divide the given number completely with no decimal digits in the quotient and with zero remainders. If you divide up this number – with one being at the start and then multiplying by two each time until it reaches its square root (which is 11.3) these numbers can be paired together to make whole factor pairs that equal 136. For example, when dividing 138 by 2 it will get 68 so (2,68) would be your pair for that equation!

## How to Find Factors of 136

Here are four methods that you can use to find the factors of 136:

- Factor of 136 using Multiplication Method.
- Factors of 136 using Division Method.
- Prime Factorization of 136.
- Factor tree of 136.

## Factors of 136 using Multiplication Method

Factors are the numbers that multiply together to form a certain number. To find out which factors belong to 136,

- We can use the multiplication method. All you have to do is take 1 and its friend (136) and join them up in pairs; then just multiply both of them together until each pair makes 136.
- That way, you’ll discover that those same two friends —1 & 136—are actually its only set of factors!

## Factors of 136 Using Division Method

To find the factors of 136 using the division method,

- Start by dividing it by its divisors starting with 1 and working your way up to divide it evenly. When you reach a number that can’t be divided into 136 anymore, then those are all the factors for this specific number – in this case, 1, 2, 4, 8 17 34 68 and136!
- This works because when an integer is multiplied together with each factor from above (1-136), it will always add up to create the original input – which was 136.

## Prime Factorization of 136

Calculate Prime Factors of

The Prime Factors of 136 =

2 x

2 x

2 x

17

To identify the prime factors of a number like 136,

- Divide it by the smallest prime number (in this case 2) and continue to do so until you can’t anymore.
- Repeating this process with 136 will give us 2 x 2 x 2 x 17 as its factorization – each one being an individual component that multiply together to create our original figure!

## Factor tree of 136

Follow the steps given below to create a factor of 136:

- To create a factor tree, start by identifying the smallest prime number of your given integer.
- Divide this number from the original and repeat this process for what remains until you find all its prime factors. For instance – 136 can be divided by 2 to give 68; since it’s not a prime, divide further using its lowest possible whole-number divisors – in our example: 4 (68 / 17) = 4 & 17(4/2)=2&17!
- By doing so, we’ve obtained two sets of numbers which when multiplied gives us back an answer equal to that of our starting point136!

## Factor Pairs of 136

Calculate Pair Factors of

1 x 136=136

2 x 68=136

4 x 34=136

8 x 17=136

17 x 8=136

34 x 4=136

68 x 2=136

So Pair Factors of 136 are

(1,136)

(2,68)

(4,34)

(8,17)

(17,8)

(34,4)

(68,2)

Understanding the concept of factor pairs can help students find solutions to many different Math problems. To determine a number’s factor pair,

- Begin by dividing it evenly by any numbers that divide into it—up until its square root is reached. Once you do this, pairing together each divisor with the result of your equation will give you all possible factors for the given integer in question.
- For example: when trying to identify all the potential combinations from 136, once divided unevenly up till 17 (its square root), 1 x 136 =136; 2 x 68 =136 and etc.—these are then considered ‘factor pairs’ because they combine to equal out exactly as expected!

Factors of 136 – Quick Recap

**Factors of 136:** 1, 2, 4, 8, 17, 34, 68, and 136.

**Negative Factors of 136:** -1, -2, -4, -8, -17, -34, -68, and -136.

**Prime Factors of 136: **2 × 2 × 2 × 17

**Prime Factorization of 136:** ** **2 × 2 × 2 × 17

Fun Facts of Factors of 136

- Understanding the properties of numbers can give us insight into complex Mathematical concepts. The number 136 is a prime example!
- It has more than two factors and therefore it’s not considered to be a prime number, however, it is still an even number and triangular in nature: when summed together its positive integers (1 + 2 + 3…+ 17) total up to equal exactly 136 itself!
- Additionally, this special composite number also happens to have 8 distinct positive factors—the smallest amount possible for any given integer–which makes understanding these core principles all the more important.

## Examples of Factor of 136

**1. There are 136 students in the school. If there are 8 desks per classroom, how many classrooms do they need? **

**Answer: **17 classrooms (136 / 8 = 17).

**2. Carl has 136 coins consisting of dimes and quarters in his piggy bank. If he has 7 times as many dimes as quarters, how many quarters does he have? **

**Answer:** 36 quarters (7 x 36 = 252; 252 – 136 = 116).

**3. John wants to divide his 136 jellybeans evenly among his friends without any leftovers. How many can each friend get if there are 9 friends altogether? **

**Answer:** 15 jellybeans (136 / 9 = 15 1/9; round up to 15).

**4. A bakery buys 136 packs of flour for $11 each, 4 cents more than the original price per pack. What was the original price of one pack of flour? **

**Answer: **7 cents ((11 – 4) / 136 =0.05).

**5. Caroline needs to cut a piece of fabric that is 136 feet long into smaller pieces that are 6 feet long each for a project at school. How many 6-foot pieces can she cut from the fabric? **

**Answer: **22 pieces (136 ÷ 6 = 22).

**6. Thomas has a lemon tree with 136 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 Wednesday? **

**Answer: **28 lemons (136 – 108 = 28). **7 . If someone buys 154 apples for $15,4 cents more than each apple costs, what was the cost for one apple? Answer: **11 cents ((15-4)/154= 0 .0775 ).

**8. A family reunion consists of 16 people so every family brings 10 food items. How many food items do they bring altogether?**

Answer:160 food items (16×10=160 )

Answer:

**9. Is 85 a factor of 136?**

**Answer:**Yes, 85 is a factor of 136 (136÷85=1 with the remainder 51 ).

**10. If someone jogs 12 laps around an oval track that measures 132 meters, how far have they run?**

**Answer:**1584 meters (132×12=1584 ).

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## Frequently Asked Questions on Factors of 136

**What is a factor of 136?**

A factor of 136 is any number that can divide 136 without leaving a remainder. The factors of 136 are 1, 2, 4, 8, 17, 34, 68, and 136.

**Is 72 a factor of 136?**

Yes, 72 is a factor of 136 (136 ÷ 72 = 1 with the remainder of 64).

**How many factors does 136 have?**

There are 8 factors for the number 136 (1, 2, 4, 8,17, 34,68, and 136).

**How can I find the prime factors of 136?**

To find the prime factors of 136, you need to list all its factors and identify which ones are prime numbers (such as 2, 3, or 5). The prime factors of 136 are 2 x 2 x 2 x 17 or 2³ x 17.

**What is the greatest common factor of 135 and 136?**

The greatest common factor (GCF) of 135 and 136 is 9 (which is 3×3)

**Can 135 be divided evenly by 132?**

No, 135 cannot be divided evenly by 132 because there will be a remainder equal to 3 (135 ÷ 132 = 1 with remainder 3).

**What is the least common multiple(LCM)of 135 and136 ?**

The least common multiple(LCM)of 135 and136 is 24360(2 x 2 x 2 x 3 x 3x 5 x 7=24360)

**What two numbers can you multiply together to get the product 135?**

You can multiply 5 x 27 or 15 x 9 to get the product 135.

**If someone has 56 quarters, how much money do they have in total?**

56 quarters equals 14 dollars ($14; 56*0.25=14 ).

**Is one a factor of every number?**

Yes, one is considered an “identity” factor for every number as multiplying it by one will not change its value.

Written by

Prerit Jain