Factors

# Factors of 103 | Prime Factorization of 103 | Factor Tree of 103

Written by Prerit Jain

Updated on: 17 Jun 2023

Contents

### Factors of 103 | Prime Factorization of 103 | Factor Tree of 103

## Factors of 103

Factors of 103 | Factor Pairs of 103 | Prime factors of 103 |

1, 103 | (1,103) | 1 and 103 |

**Factors of 103**,

**Factor Pairs of 103**,

**Prime factors of 103**

Calculate Factors of

**The Factors are**

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## What are the factors of 103

To find the factors of 103, we need to find all the numbers that divide into 103 without leaving a remainder. Here’s how we can do that:

- Start with the number 1, as it is always a factor of any number.
- Divide 103 by 2. Since 2 does not evenly divide 103, move to the next number.
- Divide 103 by 3. 3 does not evenly divide 103.
- Continue this process, dividing 103 by each subsequent number greater than 3, until you reach 103.
- Divide 103 by 4, 5, 6, 7, 8, and so on, until 103.
- Finally, divide 103 by 103 itself. 103 divides 103 evenly.
- Write down 103 as a factor: 103.
- Now, you have found all the factors of 103: 1 and 103.

## How to Find Factors of 103

Here are four methods that you can use to find the factors of 103:

- Factors of 103 using the Multiplication Method
- Factors of 103 using the Division Method
- Prime Factorization of 103
- Factor tree of 103

## Factors of 103 Using the Multiplication Method

The “multiplication method” for finding the factors of a number is a way to find all the pairs of numbers that multiply together to equal the number. Here’s how we can use the multiplication method to find the factors of 103:

- Start by writing down the number 103.
- Identify a pair of numbers whose product is equal to 103. Since 103 is a prime number, it can only be factored as 1 * 103.
- Write down these factor pairs: (1, 103).
- You have found all the factors of 103: 1 and 103.

Therefore, the factors of 103 are 1 and 103. Since 103 is a prime number, it only has two factors: 1 and itself.

## Factors of 103 through 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.

- Start by dividing 103 by the smallest prime number, which is 2. However, 2 does not divide evenly into 103.
- Move on to the next prime number, which is 3. Again, 3 does not divide evenly into 103.
- Continue dividing 103 by each subsequent prime number (5, 7, 11, 13, 17, …) until you reach the square root of 103.
- Since 103 is a prime number, it will not have any factors other than 1 and itself.

Therefore, the factors of 103 are 1 and 103.

## Prime Factorization of 103

Calculate Prime Factors of

The Prime Factors of 103 =

103

To find the prime factorization of 103, we need to find the prime factors of 103 and then list them in order. The prime factors of a number are the numbers that are only divisible by 1 and themselves. Here’s how we can find the prime factorization of 103:

- Start by dividing 103 by the smallest prime number, which is 2. However, 2 does not divide evenly into 103.
- Move on to the next prime number, which is 3. Again, 3 does not divide evenly into 103.
- Continue dividing 103 by each subsequent prime number (5, 7, 11, 13, 17, …) until you reach the square root of 103.
- Since 103 is a prime number, it cannot be divided evenly by any other prime number.
- Therefore, the prime factorization of 103 is simply 103 itself.

**In summary, the prime factorization of 103 is 103.**

## Factor tree of 103

A factor tree is a way to find the prime factors of a number by breaking it down into smaller and smaller factors until we reach the prime factors. Here’s how we can use a factor tree to find the prime factorization of 103:

- Start by writing down the number 103 at the top of the tree.
- Look for a pair of numbers whose product is equal to 103. Since 103 is a prime number, it cannot be factored any further.
- Therefore, 103 is a prime number and cannot be further factored.

The factor tree of 103 would consist of a single branch with the number 103 at the top.

Therefore, the factor tree of 103 is simply 103 itself.

## Factor Pairs of 103

Calculate Pair Factors of

1 x 103=103

So Pair Factors of 103 are

(1,103)

The factor pairs of 103 are the pairs of numbers that multiply together to equal 103. Some of the factor pairs of 103 are (1, 103).

The factor pairs of 103 can be organized into two groups: the pairs where both numbers are less than 103, and the pairs where one number is greater than 103 and the other is less than 103. The pairs where both numbers are less than 103 are called the “proper factor pairs” of 103, and the pairs where one number is greater than 103 and the other is less than 103 are called the “improper factor pairs” of 103.

## More Factors

## Factors of 103 – Quick Recap

**Factors of 103:****1 and 103****Negative Factors of 103:**-1, and -103.**Prime Factors of 103:**1 and 103**Prime Factorization of 103:**1 and 103

## Solved Examples of Factor of 103

**Q.1: Mike needs to divide a stack of 105 books into equal parts and give them away to 7 friends. How many books will each friend get? **

Solution**: **Each friend will receive 15 books since 105 is divisible by 7 (105 ÷ 7 = 15).

**Q.2:** Emma has 105 stickers and wants to split them evenly among her 5 siblings. How many stickers will each sibling receive?** Solution: **Each sibling will receive 21 stickers since 105 is divisible by 5 (105 ÷ 5 = 21).

** Q.3: Debbie wants to make 11 servings out of a cake recipe that calls for 103 grams of sugar. Is it possible?Solution:** To determine if Debbie can make 11 servings out of a cake recipe that calls for 103 grams of sugar, we need to divide the total amount of sugar by the number of servings. 103 grams of sugar / 11 servings = 9.363636…The result is a decimal number, approximately 9.3636. Since it is not a whole number, it means that each serving would require a fraction of grams of sugar, which may not be practical or accurate for measurement.

** Q.4: Keira has 104 apples and plans on giving them away in equal amounts among 8 relatives. Can she accomplish this task?Solution: **Yes, Keira can accomplish this task as 104 apples can be divided evenly into 8 parts using factors like 13 x 8 (104÷13=8, 8×13 = 104 ).

** Q.5: Sarah has 102 pencils and wants to distribute them equally among 6 friends. How many pencils will each friend get?Solution: **Each friend will receive 17 pencils since 102 is divisible by 6 (102÷6=17).

** Q.6: Alex wants to split his 102 paperclips evenly with his 3 cousins. How many paper clips will each cousin receive?Solution: **Each cousin will receive 34 paperclips since 102 is divisible by 3 (102÷3=34).

** Q.7: Tom wants to give away 105 erasers in equal amounts among 10 people. Is there a way for him still carry out his plan?Solution: **105 erasers ÷ 10 people = 10.5 erasers per person. Since 10.5 is not a whole number, it means that each person would not receive an equal number of erasers if Tom wants to give away 105 erasers. However, if Tom is allowed to distribute the erasers in a flexible manner, he could give 10 erasers to each of the 10 people, resulting in a total of 100 erasers distributed. He would then have 5 erasers remaining.

**Q.8:** Rita needs to supply the same number of toys to 9 children. What is the fewest amount of toys she needs in order for her task?**Solution:** To supply the same number of toys to 9 children, Rita needs to find the least common multiple (LCM) of the number of children, which is 9. Therefore, Rita needs a minimum of 9 toys in order to supply the same number of toys to 9 children. Each child will receive one toy.

** Q.9: Jack has 110 DVDs which he plans on giving away in equal amounts among 11 family members. Can he accomplish this task?Solution: **Yes, Jack can accomplish this task as 110 DVDs can be divided evenly into 11 parts using factors like 10 x 11 (110÷10 = 11, 11×10 = 110 ).

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## Frequently Asked Questions on Factors of 103

**What are the factors of 103?**

The factors of 103 are 1 and 103.

**What can I use to divide 103 evenly?**

Since 103 is a prime number, it only has two factors: 1 and itself. Therefore, if you divide 103 by either 1 or 103, the result will be an even division with no remainder.

**What is the prime factorization for 103?**

The prime factorization of 103 is simply 103 itself. Since 103 is a prime number, it cannot be factored into smaller prime numbers..

**Is there a way to divide 105 coins into 11 equal parts? **

105 coins ÷ 11 parts = 9.545…

Since the result is a decimal number (9.545…), it means that each part would require a fraction of coins, which is not possible when dealing with whole coins.

**Can I use 1 as a factor when dividing up 103?**

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

**Does adding all the factors add up to make the original number?**

Not necessarily, but in this case, yes – if you add all the factors together (1+3+9+13+39+103 = 168), you will get back your original number.

**John has 103 pencils and wants to split them evenly with his 5 cousins. How many pencils will each cousin receive?**

103 pencils ÷ 5 cousins = 20 pencils with a remainder of 3

Each cousin would receive 20 pencils, and there would be 3 pencils remaining.

Written by

Prerit Jain