Factors

# Factors of 104 | Prime Factorization of 104 | Factor Tree of 104

Written by Prerit Jain

Updated on: 17 Jun 2023

Contents

### Factors of 104 | Prime Factorization of 104 | Factor Tree of 104

## Factors of 104

Factors of 104 | Factor Pairs of 104 | Prime factors of 104 |

1, 2, 4, 8, 13, 26, 52, 104 | (1,104) (2,52) (4,26) (8,13) (13,8) (26,4) (52,2) | 2 x 2 x 2 x 13 |

**Factors of 104**,

**Factor Pairs of 104**,

**Prime factors of 104**

Calculate Factors of

**The Factors are**

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## What are the factors of 104

To find the factors of 104, we can start by dividing 104 by the smallest prime factor, which is 2. The result, 52, is not a prime number, so we can divide it by the next smallest prime factor, which is 2. The result, 26, is not a prime number, so we can divide it by the next smallest prime factor, which is 2. The result, 13, is a prime number, so we cannot divide it by the next smallest prime factor.

The factors of 104 are 1, 2, 4, 8, 13, 26, 52, and 104. We can organize the factors of 104 into two groups: the proper factors, which are all the factors less than 104, and the improper factors, which are all the factors including 1 and 104. The proper factors of 104 are 1, 2, 4, 8, 13, 26, and 52. The improper factors of 104 are 1, 2, 4, 8, 13, 26, 52 and 104.

## How to Find Factors of 104

The four methods that you can use to find the factors of 104 are as follows:

- Factors of 104 using the Multiplication Method
- Factors of 104 using the Division Method
- Prime Factorization of 104
- Factor tree of 104

## Factors of 104 Using the Multiplication Method

The multiplication method for finding the factors of a number involves finding pairs of numbers that multiply together to equal the number.

To find the factors of 104 using the multiplication method, we can start by finding the smallest factor, which is always 1. Next, we can find the next smallest factor by dividing 104 by 1 to get 104. Then, we can find the next smallest factor by dividing 104 by 2 to get 52, and so on until we have found all the factors of 104.

**Using this method, we can find that the factors of 104 are 1, 2, 4, 8, 13, 26, 52, and 104.**

## Factors of 104 Using the Division Method

The division method for finding the factors of a number involves dividing the number by each of its potential factors to see if the result is also a factor.

To find the factors of 104 using the division method, we can start by dividing 104 by 1. If the result is also a factor of 104, then 1 is a factor of 104. If the result is not a factor, then 1 is not a factor. We can then repeat this process with the next smallest potential factor (in this case, 2), and so on until we have found all the factors of 104.

**Using this method, we can find that the factors of 104 are 1, 2, 4, 8, 13, 26, 52, and 104.**

## Prime Factorization of 104

Calculate Prime Factors of

The Prime Factors of 104 =

2 x

2 x

2 x

13

The prime factorization of 104 can be found by dividing it by prime numbers until we can no longer divide it further. Here are the steps to find the prime factorization of 104:

- Start by dividing 104 by the smallest prime number, which is 2. 104 ÷ 2 = 52
- Continue dividing the quotient, 52, by 2. 52 ÷ 2 = 26
- Divide 26 by 2 again. 26 ÷ 2 = 13
- Now, 13 is a prime number, and we can no longer divide it further.

**Therefore, the prime factorization of 104 is 2 × 2 × 2 × 13.**

## Factor tree of 104

A factor tree is a visual representation of the prime factorization of a number. To create a factor tree for 104, we can follow these steps:

- Write the number 104 at the top of a piece of paper.
- Find the smallest prime factor of 104. In this case, it is 2.
- Write factor 2 next to the number 104, and draw a line connecting the two.
- Divide 104 by 2 to get the next number in the factor tree. In this case, the result is 52.
- Write the result, 52, next to factor 2, and draw a line connecting the two.
- Repeat this process until all the factors are prime numbers.

## Factor Pairs of 104

Calculate Pair Factors of

1 x 104=104

2 x 52=104

4 x 26=104

8 x 13=104

13 x 8=104

26 x 4=104

52 x 2=104

So Pair Factors of 104 are

(1,104)

(2,52)

(4,26)

(8,13)

(13,8)

(26,4)

(52,2)

The factor pairs of 104 are all the pairs of numbers that multiply together to equal 104. For example, one-factor pair of 104 is (1, 104), because 1 x 104 = 104. Another factor pair of 104 is (2, 52) because 2 x 52 = 104.

We can organize the factor pairs of 104 into two groups: the proper factor pairs, which are all the pairs of factors less than 104, and the improper factor pairs, which are all the pairs of factors greater than 104. The proper factor pairs of 104 are (1, 104), (2, 52), (4, 26), (8, 13), and (13, 8). The improper factor pairs of 104 are (26, 4), (52, 2), (104, 1).

## More Factors

## Factors of 104 – Quick Recap

**Factors of 104:**1, 2, 4, 8, 13, 26, 52, 104.**Negative Factors of 104:**-1, -2, -4, -8, -13, -26, -52, and -104**Prime Factors of 104:**2 × 2 × 2 × 13**Prime Factorization of 104:**2 × 2 × 2 × 13

**Also Check**: Multiples, Square Root, and LCM

## Solved Examples of Factor of 104

**Q.1: Jennifer has a box of 104 letters that she needs to divide equally among four friends. How many letters will each friend receive?****Solution: **Each friend will receive 26 letters since 104 is divisible by 4 (104÷4=26).

** Q.2: Adam bought 105 strawberries and wants to divide them into groups of three. How many groups can Adam make with his purchase?Solution: ** Adam can make 34 groups with his purchase since 104 is divisible by 3 (104÷3=34).

** Q.3: Rick has a bag of 105 seashells which he wishes to share equally amongst five family members. How many shells will each family member receive?Solution: ** Each family member will receive 21 shells since 105 is divisible by 5 (105÷5=21).

** Q.4 Harry has $105 which he needs to split evenly among himself and two friends. How much money will each person get?Solution: ** Each person will get $35 since 105 is divisible by 3 (105 ÷3 = 35).

** Q.5: Kim has an assortment of clothes with a total of 102 items, and she wants to place them into six piles evenly. How many items should each pile have?Solution: ** Each pile should have 17 items since 102 is divisible by 6 (102÷6=17).

** Q.6: Tom is baking muffins and needs to divide the batter for the recipe evenly between two people. If he has a bowl with 104 teaspoons of batter, how much batter will each person get? Solution: **Each person will get 52 teaspoons of batter since 104 is divisible by 2 (104÷2 =52 ).

** Q.7: Martha found 108 coins while walking her dog but wants to give away 11 coins in equal amounts among 10 people. Is there a way for her still carry out her plan?Solution: **Dividing 108 coins by 11 people, we get: 108 coins ÷ 11 people = 9.818181…Since the result is a decimal number (9.818181…), it means that each person would receive a fraction of coins, which is not possible when dealing with whole coins.

** Q.8: Luis has invested in a company that’s worth 1100 dollars but wants it divided equally between 11 investors. Is there a way for him still carry out his plan?Solution: **Yes, Luis can still carry out his plan if he decides to use the factors of 1100 such as 11 x 100 (1100 ÷ 11 = 100).

**Q.9:** Ahmed found 104 tennis balls at the park but wants them divided into 8 equal parts. Can he do it? **Solution: ** Yes, Ahmed can use 104’s factors such as 8×13 (104÷98 = 13) in order to divide 104 tennis balls into 8 equal parts.

** Q.10: Sarah purchased 102 pieces of candy and wants it split equally between 10 neighbours, including herself. Is this possible? Solution: ** 102 pieces of candy ÷ 10 neighbours = 10.2 pieces of candy per neighbour. Therefore, Sarah cannot split the 102 pieces of candy equally among 10 neighbours, including herself, without fractions. She would need to adjust the number of candies or the number of neighbours to achieve an equal distribution.

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## Frequently Asked Questions on Factors of 104

**What are the factors of 104?**

The factors of 104 are 1, 2, 4, 8, 13, 26, 52, and 104.

**How do you find the greatest common factor of 104 and 208?**

The prime factorization of 104 is 2 × 2 × 2 × 13.

The prime factorization of 208 is 2 × 2 × 2 × 2 × 13.

Identify the common prime factors. In this case, the common prime factors are 2 and 13.

Multiply the common prime factors to find the GCF. In this case, the GCF of 104 and 208 is 2 × 2 × 2 × 13, which is equal to 104.

**What is the prime factorization for 104?**

The prime factorization of 104 is 2 × 2 × 2 × 13, which can be written as 2³ × 13.e factorization for 104 is 22 x 23.

**Can I use 1 as a factor when dividing up 104?**

Yes, 1 is a valid factor as long as it divides up into an even or integer part.

**Tom needs to give away 108 erasers in equal amounts among 10 people. Is there a way for him still carry out his plan?**

108 erasers ÷ 10 people = 10.8 erasers per person

Since the result is a decimal number (10.8), it means that each person would receive a fraction of the erasers, which is not possible when dealing with whole erasers.

Written by by

Prerit Jain