Factors

# Factors of 112 | Prime Factorization of 112 | Factor Tree of 112

Written by Prerit Jain

Updated on: 18 Jun 2023

Contents

### Factors of 112 | Prime Factorization of 112 | Factor Tree of 112

## Factors of 112

Factors of 112 | Factor Pairs of 112 | Prime factors of 112 |

1, 2, 4, 7, 8, 14, 16, 28, 56, and 112 | (1, 112), (2, 56), (4, 28), (7, 16) and (8, 14) | 2 × 2 × 2 × 2 × 7 |

**Factors of 112**,

**Factor Pairs of 112**,

**Prime factors of 112**

Calculate Factors of

**The Factors are**

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## What are the factors of 112

The factors of 112 can be found by the following method:

- Write down the number whose factors you want to find, in this case, 112.
- Write down the number 1, as it is a factor of every number.
- Divide 112 by each number starting from 2 and going up in increments of 1 (2, 3, 4, etc.) until you reach a number that is greater than the number you are trying to factor.
- For each number, divide 112 by it and check the remainder. If there is no remainder, then the number is a factor of 112.
- Write down all the valid factors in a list.

## How to Find Factors of 112

The most significant methods of finding the factors of 112 are as follows:

- Factors of 112 using the Multiplication Method
- Factors of 112 using the Division Method
- Prime Factorization of 112
- Factor tree of 112

## Factors of 112 Using the Multiplication Method

The following are the steps through which you can find the factors of 112 through the multiplication method:

To find the factors of 112 using the multiplication method, follow these steps:

- Start with the number 1, as it is a factor of every number.
- Multiply 1 by 112. The result is 112.
- Now, look for other factors by dividing 112 by numbers greater than 1. Test divisibility by starting with 2 and moving upwards.
- Divide 112 by 2. We find that 112 ÷ 2 = 56. So, 2 and 56 are factors of 112.
- Divide 112 by 3. Since 112 is not divisible by 3, move to the next number.
- Divide 112 by 4. We find that 112 ÷ 4 = 28. So, 4 and 28 are factors of 112.
- Divide 112 by 5. Since 112 is not divisible by 5, move to the next number.
- Divide 112 by 6. Since 112 is not divisible by 6, move to the next number.
- Divide 112 by 7. We find that 112 ÷ 7 = 16. So, 7 and 16 are factors of 112.
- Divide 112 by 8. We find that 112 ÷ 8 = 14. So, 8 and 14 are factors of 112.
- Divide 112 by 9. Since 112 is not divisible by 9, move to the next number.
- Divide 112 by 10. Since 112 is not divisible by 10, move to the next number.
- Divide 112 by 11. Since 112 is not divisible by 11, move to the next number.
- Divide 112 by 12. Since 112 is not divisible by 12, move to the next number.
- Divide 112 by 13. Since 112 is not divisible by 13, move to the next number.
- Divide 112 by 14. We find that 112 ÷ 14 = 8. So, 14 and 8 are factors of 112.
- Divide 112 by 15. Since 112 is not divisible by 15, move to the next number.
- Divide 112 by 16. We find that 112 ÷ 16 = 7. So, 16 and 7 are factors of 112.
- Since we have reached the square root of 112 and have accounted for all possible factors, we can conclude the process.

**In summary, the factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.**

## Factors of 112 Using the Division Method

The factors of 112 can also be found using the division method as follows:

- Write down the number 112 and its factors 1 and 112.
- Starting with 1, divide 112 by each of its factors and check the remainder. If there is no remainder, then the factor is a valid factor of 112.

Using this method, we can see that the factors of 112 are 1, 2, 4, 8, 14, 28, 56, and 112.

Here is the complete calculation:

112 / 1 = 112 (no remainder)

112 / 2 = 56 (no remainder)

112 / 4 = 28 (no remainder)

112 / 8 = 14 (no remainder)

112 / 14 = 8 (no remainder)

112 / 28 = 4 (no remainder)

112 / 56 = 2 (no remainder)

112 / 112 = 1 (no remainder)

**Therefore, the factors of 112 are 1, 2, 4, 8, 14, 28, 56, and 112.**

This method is similar to the multiplication method, but instead of multiplying the factors to see if they produce the original number, you divide the original number by the factors to see if there is a remainder. If there is no remainder, then the factor is a valid factor of the original number.

## Prime Factorization of 112

Calculate Prime Factors of

The Prime Factors of 112 =

2 x

2 x

2 x

2 x

7

The prime factorization of 112 is as follows:

- We start by dividing 112 by the smallest prime number, which is 2. We find that 112 ÷ 2 = 56. So, the first factor is 2.
- Next, we divide 56 by the smallest prime number, which is 2. We find that 56 ÷ 2 = 28. So, the second factor is 2.
- Continuing the process, we divide 28 by 2 again. We find that 28 ÷ 2 = 14. So, the third factor is 2.
- We divide 14 by 2 once more. We find that 14 ÷ 2 = 7. So, the fourth factor is 2.
- At this point, we have reached a prime number (7), so we stop the process.

**Therefore, the prime factorization of 112 is 2 × 2 × 2× 2 × 7.**

## Factor tree of 112

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 112:

To create the factor tree for 112, we can follow these steps:

- Write down the number 112.
- Divide 112 by the smallest prime number, 2. The result is 56 with a remainder of 0.
- Divide 56 by the next smallest prime number, 2. The result is 28 with a remainder of 0.
- Divide 28 by the next smallest prime number, 2. The result is 14 with a remainder of 0.
- Divide 14 by the next smallest prime number, 2. The result is 7 with a remainder of 0.

The factor tree shows that the prime factorization of 112 is 2 x 2 x 2 x 2 x 7, which is equal to 112.

## Factor Pairs of 112

Calculate Pair Factors of

1 x 112=112

2 x 56=112

4 x 28=112

7 x 16=112

8 x 14=112

14 x 8=112

16 x 7=112

28 x 4=112

56 x 2=112

So Pair Factors of 112 are

(1,112)

(2,56)

(4,28)

(7,16)

(8,14)

(14,8)

(16,7)

(28,4)

(56,2)

A factor tree is a diagrammatic way through which the factors of a given number are presented. The following are the steps involved in that process:

- Write down the number whose factor pairs you want to find, in this case, 112.
- Write down the number 1, as it is a factor of every number.
- Divide 112 by each number starting from 2 and going up in increments of 1 (2, 3, 4, etc.) until you reach a number that is greater than the number you are trying to factor.
- For each number, divide 112 by it and check the remainder. If there is no remainder, then the number is a factor of 112.
- Write down all the valid factor pairs in a list.

Using this method, we can see that the factors of 112 are 1, 2, 4, 8, 14, 28, 56, and 112, so the factor pairs of 112 are:

(1, 112)

(2, 56)

(4, 28)

(8, 14)

(14, 8)

(28, 4)

(56, 2)

(112, 1)

## More Factors

## Factors of 112 – Quick Recap

**Factors of 112:**1, 2, 4, 7, 8, 14, 16, 28, 56 and 112.**Negative Factors of 112:**-1, -2, -4, -7, -8, -14, -16, -28, -56 and -112.**Prime Factors of 112:**2 × 2 × 2 × 2 × 7**Prime Factorization of 112:**

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

## Solved Examples of Factor of 112

**Q.1: Maria had a bag of candy that contained 132 pieces, she divided them among 6 friends. How many pieces did each friend get?****Solution:** Each friend got 22 pieces (132/6 = 22).

**Q.2:** If Alex needs to move 999 blocks from one point to another, how many times must it make the trip if the robot can carry a maximum of 111 blocks at once? ** Solution: **The robot must make nice trips (999/111 = 9).

**Q.3:** Timothy wants to display his collection of books on his shelf but his shelf can only hold 112 books. If he has 448 books, how many shelves will he need? ** Solution: **He will need 4 shelves (448/112 = 4).

**Q.**4 Sarah bought 192 items from the store and needed to purchase packing boxes that could hold 12 items each. How many boxes did Sarah need? **Solution:** Sarah needed 16 boxes (192/12 = 16).

**Q.5:** Jane wanted to buy some rope for an art project, each piece she purchased was 1 m in length and she wanted 8 m in total. How many pieces did Jane buy?** Solution: **Jane bought 8 pieces (8 x 1 = 8).

**Q.6** Mary drove 112 km on Sunday and 288 km on Monday, what was her total distance travelled over the two days? ** Solution:** Mary travelled 400 km over the two days (112 + 288 = 400).

**Q.7:** Michael needed some paint for an art project, each can cost $17, but Michael only had $187 to spend in total; how many cans of paint could Michael buy? **Solution:** Michael could buy 11 cans of paint ($187 / $17 = 11).** Q.8: Charles had 360 items that needed to be shipped using boxes that can hold 12 items per box; how many boxes will Charles need? Solution:** Charles will need 30 boxes (360/12=30).

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## Frequently Asked Questions on Factors of 112

**What are the factors of 112?**

The factors of 112 are the numbers that divide 112 without leaving a remainder. The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.

**What is the prime factorization of 112?**

The prime factorization of 112 is 2 x 2 x 2 x 2 x 7.

**How many divisors does 112 have?**

112 has 10 divisors (1, 2, 4, 8, 16, 28 32 56 64, and 112).

**Does 112 have any common factors with 60?**

The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

From the lists, we can see that the common factors of 112 and 60 are 1, 2, 4, and 8.

**Can you express 112 as a product of its prime numbers?**

Yes, you can express it as 2^4 x 7 (2x2x2x2x7).

**Is there a perfect square number that divides into 111 evenly?**

There is no perfect square number that divides into 111 evenly.

**Is there an even number that divides into 111 evenly?**

No, there is no even number that divides into 111 evenly. Since 111 is an odd number, it can only be divided evenly by other odd numbers. Even numbers cannot divide odd numbers without leaving a remainder.

**Is there a multiple of 11 in which 111 is a part of it?**

Yes, there is a multiple of 11 in which 111 is a part. The multiple of 11 that includes 111 is 11 times 10, which equals 110.

Written by

Prerit Jain