Factors of 111 | Prime Factorization of 111 | Factor Tree of 111

Factors of 111

Factors of 111	Factor Pairs of 111	Prime factors of 111
1, 3, 37, 111	(1,111) (3,37) (37,3)	3, 37

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What are the factors of 111?

The factors of 111 are 1, 3, 37, and 111. So, 111 is not a prime number, as it has more factors other than 1 and itself.

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. Prime numbers are an important concept in mathematics because they play a key role in the study of number theory and are used in various cryptographic algorithms.

How to Find Factors of 111?

You can find the factors of 111 using the following methods: 

1. Factors of 111 using the Multiplication Method
2. Factors of 111 using the Division Method
3. Prime Factorization of 111
4. Factor tree of 111

Factors of 111 Using the Multiplication Method

The factors of 111 can be found using the multiplication method as follows:

1. First, write down the number 111 and its factors, that is 1, 3, 37, and 111.
2. Next, divide 111 by each of its factors (1, 3, 37, and 111) to see if there is a remainder. If there is no remainder, then the factor is a valid factor of 111.

Using this method, you can see that 111 is only divisible by 1, 3, 37, and itself, so the factors of 111 are 1, 3, 37, and 111.

Here is the complete calculation:

111 / 1 = 111 (no remainder)

111 / 3 = 37 (no remainder)

111 / 37 = 3 (no remainder)

111 / 111 = 1 (no remainder)

Therefore, the factors of 111 are 1, 3, 37, and 111.

Factors of 111 Using the Division Method

The factors of 111 can be found using the division method as follows:

1. Write down the number whose factors you want to find. In this case, 111.
2. Write down the number 1, as it is a factor of every number.
3. Starting with 1, divide 111 by each number and go up in increments of 1 (2, 3, 4, etc.) until you reach a number that is greater than the number for which you are trying to find the factor.
4. Divide 111 by each number and check the remainder. If there is no remainder, then the number is a factor of 111.
5. Repeat this process until you have checked all the numbers up to the number, for which you are trying to find the factor.

Using this method, you can see that the only numbers that are divided by 111 without a remainder are 1, 3, 37, and 111. So, 1, 3, 37, and 111 are the factors of 111.

Prime Factorization of 111

The prime factorization of 111 is a list of all the prime numbers that can be multiplied together to get the number 111.

The factors of 111 can be found using the prime factorization method as follows:

1. Write down the number 111 and, starting from 2, check which number is completely dividing 111.
2. The number 111 can’t be completely divided by 2. So, divide 111 by 3.
3. On dividing 111 by 3, you will get the remainder as 37.
4. Since 37 is a prime number, it can’t be divided by any other number, but 37 itself.
5. On dividing 37 by 37, you will get the remainder as 1.
6. Now, 1 can’t be divided anymore.

Since 1 can’t be divided any further, the prime factors of 111 that you get after prime factorization are 3 and 37.

Factor tree of 111

A factor tree is a visual representation of the prime factorization of a number. It shows the steps taken to find the prime factors of a number by dividing the number by smaller prime numbers.

Here is the factor tree for 111:

111 | 3 | 37 | 1

To create the factor tree for 111, we can follow these steps:

1. Write down the number 111 and, starting from 2, check which number is completely dividing 111.
2. The number 111 can’t be completely divided by 2. So, divide 111 by 3.
3. On dividing 111 by 3, you will get the remainder as 37.
4. Since 37 is a prime number, it can’t be divided by any other number, but 37 itself.
5. On dividing 37 by 37, you will get the remainder as 1.
6. Now, 1 can’t be divided anymore.

The factor tree shows that the prime factorization of 111 is 3 x 37, which is equal to 111.

I hope now you know how to find the factors of 111 using different methods. If you still have any queries, you can ask them in it comments.

Factor Pairs of 111

The factor pairs of a number are all the pairs of numbers that can be multiplied together to get the original number.

To find the factor pairs of 111, we can use the following steps:

1. Write down the number 111 and its factors, that is 1, 3, 37, and 111.
2. Divide 111 by each of its factors (1, 3, 37, and 111) to see if there is a remainder. If there is no remainder, then the factor is a valid factor of 111.
3. Write down all the valid factor pairs in a list.

Using this method, you can see that the only factors of 111 are 1, 3, 37, and 111. So the factor pairs of 111 are (1, 111) and (3, 37).

More Factors

• Factors of 108
• Factors of 109
• Factors of 110
• Factors of 111
• Factors of 112
• Factors of 113
• Factors of 114

Factors of 111 – Quick Recap

• Factors of 111: 1, 3, 37, 111
• Negative Factors of 111:  -1, -3, -37, -111.
• Prime Factors of 111: 3, 37

Also Check: Multiples, Square Root, and LCM

Solved Examples of Factor of 111

Q.1: Sally had a bag of candy that contained 111 pieces, and she divided them among 3 friends. How many pieces did each friend get?
Solution: To find out the number of pieces that each friend gets, divide 111 by 3, which gives the answer as 37. (111/3 = 37). So, each friend gets 37 pieces out of 111 pieces.

Q.2: Jermaine wants to display his collection of books on his shelf, but his shelf can only hold 111 books. If he has 444 books, how many shelves will he need? 
Solution: To find out the number of shelves he will need to display his collection of books on the shelf which can only hold 111 books, and divide the total number of books he has by the number of books the shelf can hold. The total number of books = 444. On dividing 444 by 111, you will get 4. So, Jermaine will need 4 more shelves to display his collection of books.

Q.3: Jane bought 178 items from the store and needed to purchase packing boxes that could hold 11 items each. How many boxes did Jane need? 
Solution: To find out the number of boxes Jane will need to hold a total of 178 items when one box can only hold 11 items, divide the total number of items he has by the total number of items that one box can hold. The total number of items is 178. The number of items that one box can hold = 11. On dividing 178 by 111, you will get 16. So, Jane will need 16 boxes to hold 178 items.

Q.4: Adam wanted to buy some rope for an art project. Each piece he purchased was 2 m in length and he wanted 12 m in total. How many pieces did Adam buy?   
Solution: To find out the number of pieces of rope Adam bought when each piece was 2 m in length and he wanted 12 m, divide the total length he wanted by the length of one piece of rope. The total length of rope Adam wanted was 12 m. Length of one piece of rope = 2 m. On dividing 12 by 2, you will get 6. So, Adam bought 6 pieces of rope.

Q.5: Ferdinand needed some paint for an art project. Each can cost $15, but Ferdinand only had $165 to spend in total. How many cans of paint could Ferdinand buy?
Solution: To find out the number of cans of paint Ferdinand could buy when one can of paint cost $15 and Ferdinand only had $165, divide the total amount Ferdinand had by the amount of one can of paint. The total amount Ferdinand had = $165. The amount of one can of paint = $15. On dividing 165 by 15, you will get 11. So, Ferdinand will need to buy 11 cans of paint.

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Frequently Asked Questions on Factors of 111