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

Factors are the natural numbers that are capable of dividing a number evenly, without leaving any remainder behind. Another way to think about factors is as the integers that, when they are present in pairs, multiply to produce the original number.
Factors of seven

Figure 1 – All possible Factors of 7

Factors of 7 are the collection of both positive and negative integers that, when undergoing division, divide 7 completely, and the only thing left behind is a perfect whole-number quotient. Also, factors of the number 7 are referred to as its perfect divisors. An interesting fact about the factors of 7, just like the factors of any other number, cannot be expressed as fractional numbers The usual methods used to find the factors of any given integer are division and 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. 

What Are the Factors of 7?

The factors of the number 7 are 1 and 7, respectively.  Given that, 7 being an odd prime number in nature serves to have just two well-recognized factors, just like all the other prime numbers.  An interesting fact about the factors of 7 is that both the numbers 1 and 7 are prime and the greatest factor amongst the two is 7 itself.  

How To Calculate the Factors of 7?

You can calculate the factors of 7 by using the two widely used techniques, division, and multiplication According to the general 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 by nature, just two factors have to be determined.  Let’s see how the laws of division work to calculate the factors of the number 7.  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? 
Division method of seven

Figure 2 – Division method of 7

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 the universal factor, as every number is divisible by 1.   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?
Division process of seven

Figure 3 – Division process of 7

Yes, the quotient resulting from the above division, i.e., 1, is a perfect whole-number. Also, no remainder is left behind. Hence, 1 and 7 are the factors of 7.  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-multiplication is employed.

1 x 7 = 7

7 x 1 = 7

The factors of 7 can be positive as well as negative. The negative factors are the numbers that are written with a negative sign. The negative factors of 7, when multiplied in pairs, produce 7 as a result. It can be said that negative factors are nothing but the same as positive factors with opposite signs. Hence, the negative factors of 7 are referred to as the additive inverse 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 factorization is the method that focuses on dividing an integer evenly into its prime factors until the result is 1.  The process for evaluating the prime factors of a given number by using the prime factorization technique includes the upside-down division methodology to serve as the primary approach where the division continues until the end quotient received is 1 Prime factors 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 called prime factors The prime factorization of the number 7 is given as follows:
Prime factorization of seven

Figure 4 – Prime Factorization of 7

Also, the prime factorization of 7 can be expressed as the following expression:

1 x 7 = 7

Hence, there are prime factors of 7.  The prime factors of 7 are also termed as the distinct prime factors such that there are only distinct factors of the number 7.  Distinct Prime Factors of 7 = 1, 7  Greatest Common Divisor(GCD) and Least Common Divisor(LCD) are the two important terminologies that are to be considered while calculating the factors of any two given numbers.  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.  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. 

Factor Tree of 7

A method for visually expressing a number’s factors, particularly the prime factors, is the 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 the type of a number. It may indicate if an integer is prime, square, or cubic. The LCD and GCD may also be calculated using the factor tree. The following steps are to be adopted to construct the factor tree of any given number:
  1. Place the given number at the top.
  2. Construct the branches of a tree. 
  3. Mention the prime factors of the given number on each branch.
  4. Terminate the process by placing the prime factors of the smallest possible number that can have prime factors.  
The following figure shows the factor tree of the number 7.
Factor tree of seven

Figure 5 – Factor Tree of 7

It is visible from the factor tree that the number 7 is prime

Factors of 7 in Pairs

The groups of numbers known as factor pairs are those that, when multiplied together, provide the same outcome as the product of which they are a factor. Both a collection of negative and positive integers may make up the pair of factors. The method used to determine the 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

Where (1, 7) is a positive factor pair of 7. Similarly, 

-1 x -7 = 7

Where (-1, -7) is a negative factor pair 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

Such as remembering the factor pairs of 7.   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.   Therefore:

m = 7 

In simple words, we can say that Ana sold 7 pencils in 1 day. 

Example 2

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

Solution

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

1 + 7 = 8

Therefore the sum of its factor is 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.  Images/mathematical drawings are created with GeoGebra. 

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