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Factors of 25: Prime Factorization, Methods, Tree, and Examples 

Factors of 25 refer to the numbers that, when multiplied together, produce a result of 25, or they are the numbers by which 25 may be divided. As a result, a number is said to be a factor if it divides 25 with a remainder of 0. 

Make a list of all the integers that are smaller than or equal to the number you are seeking for factors to examine its factors. For instance, the number 25 will fall between 1 and 5.  In this situation, dividing each of them will reveal the solution. 

An intriguing fact regarding factors is the statement that two is the factor of all numbers. That being said, the factors of a number can be found using division and multiplication. However,  there are several methods for locating integer factors.  

There are even simpler ways to figure out a number’s factors. The quotient and the divisor are regarded as factors of the supplied number once the remainder equals zero, which can be achieved by simply diluting the number itself until the residual equals zero. 

Let’s use one of these situations as an illustration. The outcome of 25 divided by 5 is 5. As a  result, both the solution and the divisor are regarded as factors. They are referred to as factor pairs as a whole, i.e. (5, 5). 

In this article, you will acquire a brief overview of the factors 25. The content of this article includes information on simple methods for determining and calculating the factors of 25 as well as interesting tidbits you might not have known. 

What Are the Factors of 25?

The factors of 25 are 1, 5, and 25, and as the number has more than 1 factor, it shows that it is a composite number. These factors can all be paired together to form factor pairs. 

You can achieve it by pairing the numbers so that the result is 25. When 25 is divided by these figures, there will never be any remainder other than zero.

How to Calculate the Factors of 25?

To calculate the factors of 25, we may use a straightforward division method to obtain the factors of 25. Let’s move on to the procedure. 

The smallest divisor you can find to divide 25 by is 1. Given this, 1 is one of the factors of 25.  The next whole number is then tested to see if it can successfully split 25 in half. 

\[ \frac{25}{2} = 12.5\]

This shows that 2 is not a factor of 25 as the answer is a decimal number. Similarly, 3 and 4 are also not the factors of 25. 

\[ \frac{25}{3} = 8.33\]

\[ \frac{25}{4} = 6.25\]

So, we move on to 5. 5 is a factor of 25 because the answer is a whole number.  25/5 = 5 

We can stop dividing by whole numbers once we reach 25/25 = 1. Because of this, we cannot use any more whole numbers. The factors of 25 determined via division are as follows: 

\[ \frac{25}{25} = 1\]

\[ \frac{25}{5} = 5\]

\[ \frac{25}{1} = 25\]

Therefore, all the factors of 25 are 1, 5, and 25. 

Focusing on multiplication to find factors of 25. Think about 25 as the outcome of two whole numbers in every sense. Every single integer that appears in any one of these products is a  factor of 25. The examples are given below: 

1×25 = 25 

5×5 = 25 

25×1 = 25 

Henceforth, these are the three factors of 25. 

Factors of 25 by Prime Factorization

Prime Factorization is the one way to express a certain number as the product of its prime factors. It involves determining which prime factors can multiply with one another to get the number as a product. 

It is a method for figuring out or displaying a given integer as the sum of prime integers, to put it another way. A prime number simply has two factors: 1 and the number itself. 

Since 25 is a composite number, it should contain prime factors. Let’s learn how to recognize the key factors. First, divide 25 by the smallest prime factor; for this example, let’s pick 2. 25/2  will provide a fractional number when split, thus we may move on to the following prime number, which is 3. It is therefore not a factor. 

After, checking out the number 4 (which is not a factor), we move on to 5. 

\[ \frac{25}{5} = 5\]

Thus, 5 is a prime factor. 

\[ \frac{5}{5} = 1\]

As we got 1 now, so we cannot proceed further. The only prime factor of 25 is 5. Hence, the prime factorization of 25 is 5 x 5, making 25 a perfect square. 

The diagram for the Factors of 25 using Prime Factorization is attached below:

Figure 1

Factor Tree of 25

Even a number’s factors can be expressed in a variety of ways. Expressing factors as a Factor  Tree is only one of the many ways to graphically depict a number’s prime factors. The root of the factor tree is the actual number, and the branches that branch off from it stand in for factors until you reach the prime number.  

Therefore, 5 is the only prime factor of 25 as determined by prime factorization.

You can take a look at the Factor Tree of 25 below:

Figure 2

Given below are the fun facts about the perfect square number 25: 

  1. The sum of the five single-digit odd natural numbers 1, 3, 5, 7, and 9 results in 25. 2. 25 is an automorphic number, a centered octagonal number, a centered square number, an octahedral number, and a centered octagonal number. Additionally, it is a  vertically symmetrical number and a Cullen number. 
  2. 25 is the manganese atom’s atomic number. Moreover, the typical percentage of a  person’s DNA that is shared by a person and their half-sibling, grandparent, grandchild,  aunt, uncle, niece, nephew, and identical twin cousin (offspring of identical twins) or double cousin.
  3. The number of points required to win a set of volleyball using rally scoring rules (apart from the fifth set), as long as the losing team’s score is two lower than the winning team’s score. 
  4. A maximum of 25 new football players may receive athletic scholarships from institutions that are NCAA Division I FBS members in the United States. 
  5. The annual World Pasta Day is celebrated on October 25. 
  6. Hindi’s translation of the name of India’s national board game, “Pachisi” is “25.”  Furthermore, 25 is the duration of the marriage as indicated by a silver wedding anniversary. 
  7. 25 is the number of French department Doubs. 
  8. 25 is the name of an Irish card game and it is also the name of Adele’s album that was released in 2015. 
  9. The team’s finest slugger often wears the number 25 in baseball. Also, 25 was the size of a Major League Baseball team’s full roster before 2020 for most of the season.     

    Factors of 25 in Pairs

    Factor pairs of 25 are a pair of numbers that when multiplied together equal 25. The factors are  as follows: 

    If 1×25=25, then (1, 25) is the pair factor of 25. Similarly, let’s look at more pairs: 

    1 × 25 = 25, (1, 25) is a pair factor of 25. 

    5 × 5 = 25, (5, 5) is a pair factor of 25. 

    25 × 1 = 25, (25, 1) is a pair factor of 25. 

These are the positive factor pairs of 25. To find out the negative factor pair, all you have to do is to reverse the signs. The negative factor pairs are as follows: 

If -1 × -25 = 25, then (-1, – 25) is a pair factor of 25. 

-1 × -25 = 25, (-1, -25) is a pair factor of 25. 

-5 × -5 = 25, (-5, -5) is a pair factor of 25. 

-25 × -1 = 25, (-25, -1) is a pair factor of 25. 

Thus, given above are the negative pair factors of the integer 25. 

Factors of 25 Solved Examples

Example 1

Find the common factors of 20 and 25. 

Solution 

The factor of 20: 1, 2, 4, 5, 10, and 20. 

The factor of 25: 1, 5, and 25. 

Therefore, the common factors between 20 and 25 are 1 and 5. 

Example 2

Bob was instructed to identify a number that is not a factor of 25 out of a set of numbers.  Find that number for bob, please.  

The list of the numbers is given below: 

2, 5, 7, 11, 15, 25 

Solution 

Although 1, 5, and 25 are the factors of 25, there is a remainder left when 25 is divided by 6, 8, and 9. In light of this, 6, 8, and 9 are not the factors of 25, while 1, 5, and 25 are. 

Example 3

A set of 25 plates is pulled out by Sophie from the kitchen cabinet and placed on the lunch table. How many different ways can she arrange them? 

Solution 

The factors of 25 must be known to solve this issue. Make a list: 1, 5, and 25. Therefore  the factor pairs are as follows: 

(1, 25)  

(5, 5) 

The first pair, 1 and 25, does not provide much information. Just one tack of 25 plates is all that it means. However, according to the second pair, we may have five stacks of five plates.

All images/mathematical drawings are made using GeoGebra.

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