# Factors of 112

Factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112

#### How to find factors of a number

 1.   Find factors of 112 using Division Method 2.   Find factors of 112 using Prime Factorization 3.   Find factors of 112 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 112

• Divide 112 by 1: 112 ÷ 1 : Remainder = 0
• Divide 112 by 2: 112 ÷ 2 : Remainder = 0
• Divide 112 by 4: 112 ÷ 4 : Remainder = 0
• Divide 112 by 7: 112 ÷ 7 : Remainder = 0
• Divide 112 by 8: 112 ÷ 8 : Remainder = 0
• Divide 112 by 14: 112 ÷ 14 : Remainder = 0
• Divide 112 by 16: 112 ÷ 16 : Remainder = 0
• Divide 112 by 28: 112 ÷ 28 : Remainder = 0
• Divide 112 by 56: 112 ÷ 56 : Remainder = 0
• Divide 112 by 112: 112 ÷ 112 : Remainder = 0

Hence, Factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112

#### 2. Steps to find factors of 112 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 112 using the division method, follow these steps:

• Step 1. Start dividing 112 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 112, which is 2. Divide 112 by 2 to obtain the quotient (56).
112 ÷ 2 = 56
• Step 3. Repeat step 1 with the obtained quotient (56).
56 ÷ 2 = 28
28 ÷ 2 = 14
14 ÷ 2 = 7
7 ÷ 7 = 1

So, the prime factorization of 112 is, 112 = 2 x 2 x 2 x 2 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 112 as shown below:

So, the prime factorization of 112 is, 112 = 2 x 2 x 2 x 2 x 7.

#### 3. Find factors of 112 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 112 would be the two numbers which, when multiplied, give 112 as the result.

The following table represents the calculation of factors of 112 in pairs:

Factor Pair Pair Factorization
1 and 112 1 x 112 = 112
2 and 56 2 x 56 = 112
4 and 28 4 x 28 = 112
7 and 16 7 x 16 = 112
8 and 14 8 x 14 = 112

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 112. They are called negative pair factors.

Hence, the negative pairs of 112 would be ( -1 , -112 ) , ( -2 , -56 ) , ( -4 , -28 ) , ( -7 , -16 ) and ( -8 , -14 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 112 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 112.
• Every number is a factor of zero (0), since 112 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 4, 7, 8, 14, 16, 28, 56, 112 are exact divisors of 112.
• Factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112. Each factor divides 112 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 7, 8, 14, 16, 28, 56, 112 are all less than or equal to 112.

• Is 112 a perfect square?

No 112 is not a perfect square.

• What are factors of 112?

Factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112.

• Which is greatest factor of 112?

The greatest factor of 112 is 56.

• What is the sum of all factors of 112?

The sum of all factors of 112 is 248.

• What are multiples of 112?

First five multiples of 112 are 224, 336, 448, 560.

• What is the greatest prime factors of 112?

The greatest prime factor of 112 is 7.

• What are six multiples of 112?

First five multiples of 112 are 224, 336, 448, 560, 672, 784.

• What is prime factorization of 112?

Prime factorization of 112 is 2 x 2 x 2 x 2 x 7.

• Is 112 a whole number?

Yes 112 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 112? Help her in writing all the factors.

Positive factors are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112.
Negative factors are -1, -2, -4, -7, -8, -14, -16, -28, -56, -112.

Can you help Sammy find out the product of the odd factors of 112?

Factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112.
Odd factors of 112 are 1, 7.
Hence product of odd factors of 112 is; 1 x 7 = 7.

Joey wants to write all the prime factors of 112 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 112 are 2, 2, 2, 2, 7.
So in exponential form it can be written as 24 x 7.

How many factors are there for 112?

Factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112.
So there are in total 10 factors.

Kevin has been asked to write 9 factor(s) of 112. Can you predict the answer?

9 factor(s) of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56.

Sammy is puzzled while calculating the prime factors of 112. Can you help him find them?

Factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112.
Prime factors of 112 are 2, 2, 2, 2, 7

What is prime factorization of 112?

Prime factorization of 112 is 2 x 2 x 2 x 2 x 7 = 24 x 7.