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Factors

Factors of 56 | Prime Factorization of 56 | Factor Tree of 56

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

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Factors of 56 | Prime Factorization of 56 | Factor Tree of 56

Factors of 56 | Prime Factorization of 56 | Factor Tree of 56

Factors of 56: The factors of a number are a list of integers, that divide the given number evenly. The number we will be examining today is 56.

56 has a total of 8 factors. Factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.


The factors of 56 are both positive and negative. They are also written as pairs. Multiplying the numbers within the pairs will give 56 as the product.

In this article, we will find the factors of 56 using the division method, prime factorization, and the factor tree method. We will also look at solved examples. Continue reading to learn more.

What Are the Factors of 56?

The factors of 56 are those numbers that can divide 56 evenly. They leave no reminders. These factors can also be positive or negative.

Factors of 56: 1, 2, 4, 7, 8, 14, 28 and 56
Negative Factors of 56: –1, -2, -4, -7, -8, -14, -28 and -56
Prime Factorization of 56: 2 X 2 X 2 X 7 or 23 X 7
Pair Factors of 56: (1, 56); (2, 28); (4, 14) and (7, 8)
Prime Factors of 56: 2, 7
Sum of Factors of 56: 120
Sum of Prime Factors of 56: 9
Factors of 56

What Are the Factors of 56 in Pairs?

The pair factors of 56 are a set of numbers when multiplied together yield 56 as the product. These pair factors can be presented as positive and negative pairs. This is shown in the table below:

Positive Pair Factors of 56

Positive pair factors of 56: (1, 56); (2, 28); (4, 14) and (7, 8).

Positive Pair Factors of 56

Negative Pair Factors of 56

Negative pair factors of 56: (-1, -56); (-2, -28); (-4, -14) and (-7, -8).

Negative Pair Factors of 56

How To Find Factors of 56 Through Division Method?

We will first use the division method to determine the factors of 56. According to this method, we will multiply 56 by a sequence of numbers.

The factors of 56 are those numbers that divide it evenly, without leaving reminders. The steps below explain the division method in a detailed manner:


• 56 ÷ 1 = 56
• 56 ÷ 2 = 28
• 56 ÷ 4 = 14
• 56 ÷ 7 = 8
• 56 ÷ 8 = 7
• 56 ÷ 14 = 4
• 56 ÷ 28 = 2
• 56 ÷ 56 = 1


We can observe that 1, 2, 4, 7, 8, 14, 28, and 56 are the numbers that leave no remainders when divided by 56. Hence, they are the factors of 56.

What Is the Prime Factorization of 56?


Before we perform the prime factorization method, we must check if the given number is a prime/ composite number. If it is a prime number, it has only two factors: 1 and 56. If the number is composite, then it has more than two factors.
56 is the composite number. So, we have more than two factors. Thus, we can use the prime factorization method to find the factors of 56.


The steps to find prime factors of 56 using the prime factorization method are given below:


Step 1: Divide the number 56 by the smallest prime number that can divide it. The smallest prime number that divides 56 is 2.
56 ÷ 2 = 28


Step 2: Divide the quotient 28 by the smallest prime number, which is 2.
28 ÷ 2 = 14


Step 3: Repeat the process until you get the number prime number as the quotient.
14 ÷ 2 = 7


Step 4: We got 7 as the quotient. Since it is a prime number, it can be divided only by itself.
7 ÷ 7 = 1
The quotient is 1. We know that 1 cannot be divided further.

So, the prime factors of 56 are 2 X 2 X 2 X 7 or 23 X 7.

We can also write it down as 2 and 7, as both of them are prime numbers.


Image representation of the prime factorization of 56:

Prime Factorization of 56

What is the Factor Tree of 56?

The factor tree is another method we can use to determine the factors of 56. As per this approach, we will first place the number 56 on top of the factor tree. We will branch it out to one of the pair factors of 56. We will further divide these factors until all the branches of the factor tree are prime numbers.


Step 1: Place the number 56 on top of the factor tree. As part of its branches, write one of the pair factors of 56- 2 and 28.


Step 2: 2 is a prime number and it cannot be separated any further. We will now divide 28 into 2 and 14.


Step 3: 2 is a prime number but 14 is not. So, we will split 14 into 2 and 7.


Step 4: We can see that 2 and 7 are both prime numbers. The factor tree ends here.


Hence, circling all the branches, 23 X 7 or 2 X 2 X 2 X 7 = 56, which are 56 prime factors.


We can write the factor tree of 56 in many ways.

Below is an image representation of the factor tree of 56

Factor tree of 56

Solved Examples on Factors of 56

Here are some solved examples of 56 factors:

What is the sum of all the factors of 56?
1, 2, 4, 7, 8, 14, 28, and 56 are the 56 factors.
1 + 2 + 4 + 7 + 8 + 14 + 28 + 56 = 120
Hence, 120 is the sum of all 56 factors.

What are the factors and prime factors of 56?
The factors of 56: 1, 2, 4, 7, 8, 14, 28, and 56.
The prime factors of 56: 23 X 7 or 2 X 2 X 2 X 7.

What’s the highest common factor between 35 and 56?
The factors of 35 are 1, 5, 7, and 35.
Factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.
Hence, from the above, the common factors of 35 and 56 are 1 and 7.
The highest common factor between 35 and 56 is 7.

What’s the highest common factor between 63 and 56?
The factors of 63 are 1, 3, 7, 9, 21, and 63.
Factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56.
Hence, from the above, the common factors of 63 and 56 are 1 and 7.
The highest common factor between 63 and 56 is 7.

Is 8 a factor of 56?
Yes, 8 is a factor of 56.
As 56 ÷ 7 = 8.

What are the factors of -56?
The factors of -56 are -1, -2, -4, -7, -8, -14, -28, and -56.

What are the common factors of 84 and 56?
To find the common factors of 84 and 56, we need to find the factors of both numbers.
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84
Factors of 56: 1, 2, 4, 7, 8, 14, 28 and 56
Hence the common factors of 84 and 56 are 1, 2, 4, 7, 14, and 28.

What are all the factors of 56?
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.

What are the factors of 56 that are composite?
Any number which has more than 2 factors is known as a composite number.
The list of number which has more than 2 factors in factors of 56 is 4, 8, 14, 28 and 56.

What factors of 56 are multiples of 2?
The factors of 56 that are multiples of 2 are 2, 4, 8, 14, 28, and 56.
2 x 1 = 2
2 x 2 = 4
2 x 4 = 8
2 x 7 = 14
2 x 14 = 28
2 x 28 = 56.

How many 56 factors are odd?
A total of 2 odd numbers are there in factors of 56 and they are 1 and 7.

What are the factors of 28 and 56?
The factors of 28 are 1, 2, 4, 7, 14, and 28.
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.

How many different factors are there for the number 56?
A total of 8 factors are there for the number 56 and they are 1, 2, 4, 7, 8, 14, 28, and 56.

How many pair factors are there in 56?
A total of 4 pairs are there in factors of 56.

What is the largest factor of 56?
The largest factor of 56 is 56.
The second largest factor of 56 is 28.

FAQs on Factors of 56

List all the factors of 56
1, 2, 4, 7, 8, 14, 28, and 56 are the 56 factors.

What are the composite factors of 56?
4, 8, 14, 28, and 56 are the 56 composite factors.
Composite factors are those that have more than 2 factors other than 1 and itself.

What are the factors of 56 in pairs?
(1, 56); (2, 28); (4, 14), and (7, 8) are the 56 factors of pairs.

What are the positive factors for 56?
1, 2, 4, 7, 8, 14, 28, and 56 are the positive factors for 56.

List the first 10 multiples of 56.
Multiples are those numbers, which can be divided by another given number evenly.
First 10 multiples of 56: 56, 112, 168, 224, 280, 336, 392, 448, 504, and 560

We have covered all the necessary aspects of the factors 56. We hope that this blog has been informational and easy to understand.

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Prerit Jain

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