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# Factors of 7: Prime Factorization, Methods, Tree, and Examples

**FactorsÂ**are the natural numbers that are capable ofÂ

**dividing a number evenly**, without leaving any remainder behind. Another way to think about factors is as the integers that, when they areÂ

**present in pairs**, multiply to produce the original number.

**Factors of 7**Â are the collection of bothÂ

**positiveÂ**andÂ

**negative**Â integers that, when undergoing division, divide 7 completely, and the only thing left behind is aÂ

**perfect whole-number quotient**. Also, factors of the number 7 are referred to as its perfectÂ

**divisors**. An interesting fact about the factors of 7, just like the factors of any other number, cannot be expressed asÂ

**fractional numbers**.Â The usual methods used to find the factors of any given integer areÂ

**divisionÂ**andÂ

**multiplication methods**. Prime factorization and factor tree, on the other hand, are two straightforward methods that employ division and multiplication as their primary techniques for finding the necessary factors. In this article, we will find how to calculate the factors of 7, its prime factorization, factor tree, and pairs of factors.Â

## What Are the Factors of 7?

**The factors of the number 7 are 1 and 7, respectively.Â**Given that, 7 being anÂ

**odd prime number**Â in nature serves to have just two well-recognized factors, just like all the other prime numbers.Â An interesting fact about the factors of 7 is that both the numbers 1 and 7 areÂ

**prime**and theÂ

**greatest factor**Â amongst the two is 7 itself.Â Â

## How To Calculate the Factors of 7?

You can calculate the factors of 7 by using the two widely used techniques,Â**division**, and

**multiplication**.Â According to the general

**Â laws of mathematics**, division is the most commonly used approach to computing the factors of a number. Every time you want to calculate the factors of a number, conduct a completely separate division process for each of them. Luckily, 7 is a

**highly prime number**Â by nature, justÂ

**two factors**Â have to be determined.Â Let’s see how the laws of division work to calculate the factors of the number 7.Â First, make a list of all the numbers that 7 may be divided by. The suggested numbers that are less than or equal to 7 should be divided by 7. Verify the values of the quotient and the remainder. Is the remainder 0 and the quotient a perfect whole number? For startups, let’s divide 7 by the smallest divisible factor, i.e., 1. Check for the remainder. Is the remainder zero? Is the quotient a perfect whole number?Â Yes, the quotient resulting from the above division i.e. 7, is a perfect whole-number. Also, no remainder is left behind. Also, the number 1 is known as theÂ

**universal factor**, as every number is divisible by 1.Â Â Now, moving towards the greatest possible factor, i.e., 7. Check for the remainder. Is the remainder zero? Is the quotient, a perfect whole number? Yes, the quotient resulting from the above division, i.e., 1, is a perfect whole-number. Also, no remainder is left behind. Hence,Â

**1**Â and

**Â 7**Â are the factors of 7.Â By the above-mentioned approach, multiplication is another technique that you can use to find the required factors list of 7. As the main strategy,

**pair-multiplicationÂ**is employed.

**1 x 7 = 7**

**7 x 1 = 7**

**additive inverseÂ**of its positive factors. Given below is the list of the positive and negative factors of 7:

**Positive Factors of 7 = 1, 7**

**Negative Factors of 7 = -1, -7**

## Factors of 7 by Prime Factorization

**Prime factorizationÂ**is the method that focuses on dividing an integer evenly into its prime factors until the result is 1.Â The process for evaluating the prime factors of a given number by using the prime factorization technique includes the

**Â upside-down division methodologyÂ**to serve as the primary approach where the division continues until the

**Â end quotient**Â received isÂ

**1**.Â

**Prime factors**Â are integers or numbers that can only be divided evenly by one and by themselves. The prime factor of a given integer can be any number that is only divisible by 1 and themselves. The factors which are prime numbers are calledÂ

**prime factors**.Â The prime factorization of the number 7 is given as follows: Also, the prime factorization of 7 can be expressed as the following expression:

**1 x 7 = 7**

**2Â**prime factors of 7.Â The prime factors of 7 are also termed as theÂ

**distinct prime factors**Â such that there are onlyÂ

**2Â**distinct factors of the number 7.Â

**Distinct Prime Factors of 7 = 1, 7Â**

**Greatest Common Divisor**(GCD) andÂ

**Least Common Divisor**(LCD) are the two important terminologies that are to be considered while calculating the factors of any two given numbers.Â Greatest Common Divisor (GCD), also known as the Greatest Common Factor (GCF), is the largest number amongst the factors of any two non-zero numbers.Â Similarly, Least Common Divisor (LCD), also known as the Least Common Multiple (LCM), is the smallest number amongst the factors of any two non-zero numbers.Â

## Factor Tree of 7

A method for visually expressing a number’s factors, particularly the prime factors, is theÂ**factor tree**. It is called a factor tree because it resembles a tree with many branches that are joined at the base. A factor tree is used to determine theÂ

**typeÂ**of a number. It may indicate if an integer is prime, square, or cubic. TheÂ

**LCDÂ**andÂ

**GCD**Â may also be calculated using the factor tree. The following steps are to be adopted to construct the factor tree of any given number:

- Place the given number at the top.
- Construct the branches of a tree.Â
- Mention the prime factors of the given number on each branch.
- Terminate the process by placing the prime factors of the smallest possible number that can have prime factors.Â Â

**prime**.Â

## Factors of 7 in Pairs

The groups of numbers known asÂ**factor pairs**Â are those that, when multiplied together, provide the same outcome as the product of which they are a factor. Both a collection ofÂ

**negativeÂ**andÂ

**positiveÂ**integers may make up the pair of factors. The method used to determine theÂ

**factor pair**of 7 is identical to the approach used to determine the factor pairs of any other number. Factor pairs can be both positive and negative but can never be a figure that is non-whole numbers. Hence, the pair of factors of the number 7 are represented as:

**1 x 7 = 7**

**(1, 7)**Â is aÂ

**positive factor pair**Â of 7. Similarly,Â

**-1 x -7 = 7**

**(-1, -7)**Â is aÂ

**negative factor pair**Â of 7.

## Factors of 7 Solved Examples

Now, let us solve a few examples to test our understanding of the above article.### Example 1

Ana bought 7 pencils, out of which she sold (m) number of pencils in 1 day. Can you find the correct number of sold pencils?### Solution

According to the given statement:**7/m = 1**

**7 = 1 x m**

**Â Factor Pairs of 7 = (1, 7)**From the aforementioned list, we can clearly state that 1, when paired with 7, results in producing 7 as the result of the multiplication.Â Â Therefore:

**m = 7Â **

### Example 2

Sarah wants to calculate the sum of the positive factors by 7. Can you help her in finding the correct answer?Â### Solution

The positive factors of 7 are given as follows:Â**Factors of 7 = 1, 7**Hence, the sum of the positive factors of 7 is given as follows:

**1 + 7 = 8**

### Example 3

Emily wants to find out the GCF of factors 7 and 14. Can you help her in finding the correct answer?### Solution

The following is the list of factors 7:**Factors of 7 = 1, 7**The following is the list of factors of 14:

**Factors of 14 = 1, 2, 7, 14**There are two common factors amongst the factors of 7 and 14 are 1 and 7. Also, the GCF of factors of 7 and 14 is 7, respectively.Â

*Images/mathematical drawings are created with GeoGebra.Â*

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