# Factors of 56

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

#### How to find factors of a number

 1.   Find factors of 56 using Division Method 2.   Find factors of 56 using Prime Factorization 3.   Find factors of 56 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 56

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

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

#### 2. Steps to find factors of 56 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 56 using the division method, follow these steps:

• Step 1. Start dividing 56 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 56, which is 2. Divide 56 by 2 to obtain the quotient (28).
56 ÷ 2 = 28
• Step 3. Repeat step 1 with the obtained quotient (28).
28 ÷ 2 = 14
14 ÷ 2 = 7
7 ÷ 7 = 1

So, the prime factorization of 56 is, 56 = 2 x 2 x 2 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 56 as shown below:

So, the prime factorization of 56 is, 56 = 2 x 2 x 2 x 7.

#### 3. Find factors of 56 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 56 would be the two numbers which, when multiplied, give 56 as the result.

The following table represents the calculation of factors of 56 in pairs:

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

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 56. They are called negative pair factors.

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

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 56 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 56.
• Every number is a factor of zero (0), since 56 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, 28, 56 are exact divisors of 56.
• Factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56. Each factor divides 56 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 7, 8, 14, 28, 56 are all less than or equal to 56.

• What two numbers make 56?

Two numbers that make 56 are 2 and 28.

• What is prime factorization of 56?

Prime factorization of 56 is 2 x 2 x 2 x 7.

• Write some multiples of 56?

First five multiples of 56 are 112, 168, 224, 280.

• Which is the smallest prime factor of 56?

The smallest prime factor of 56 is 2.

• Is 56 a perfect square?

No 56 is not a perfect square.

• What is the sum of all factors of 56?

The sum of all factors of 56 is 120.

• What are factors of 56?

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

• How do you find factors of a negative number? ( eg. -56 )?

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

• Is 56 a whole number?

Yes 56 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 56. Help him in finding the mean of 56.

Factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 56 is 1 + 2 + 4 + 7 + 8 + 14 + 28 + 56 = 120.
Hence, the mean of factors of 56 is 120 ÷ 8 = 15.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 56? Help her in writing all the factors.

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

Joey wants to write all the prime factors of 56 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 56 are 2, 2, 2, 7.
So in exponential form it can be written as 23 x 7.

Kevin has been asked to write 7 factor(s) of 56. Can you predict the answer?

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

Sammy is puzzled while calculating the prime factors of 56. Can you help him find them?

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

What is prime factorization of 56?

Prime factorization of 56 is 2 x 2 x 2 x 7 = 23 x 7.

Can you help Rubel to find out the product of the even factors of 56?

Factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56.
Even factors of 56 are 2, 4, 8, 14, 28, 56.
Hence, product of even factors of 56 is; 2 x 4 x 8 x 14 x 28 x 56 = 1404928.