What are the Factors of 25?
Factors of a number are the product of such numbers which completely divide the given number. Factors of a given number can be either positive or negative numbers. By multiplying the factors of a number we get the original number. For example 1, 2, 3, 6 are the factors of 6. On multiplying two or more numbers we get 6. Hence we have 2 x 3 = 6 or 1 x 6 = 6. On this page, we will study the factors of 25 definitions, what are the factors of 25, what is the prime factorization of 25, factor tree of 25, and examples. Factor pairs of the number 25 are the pairs of the whole numbers which could be either positive or negative but not a fraction or decimal number. Factorisation is the common method to find the factors of 25. Let us study the prime factorization of 25.
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Factors of 25 Definition
The factors of a number are defined as the numbers which when multiplied will give the original number, by multiplying the two factors we get the result as the original number. The factors can be either positive or negative integers.
Factors of 25 are all the integers that can evenly divide the given number 25.
Now let us study how to calculate all factors of 25.
What are the Factors of 25?
According to the definition of factors of 25, we know that factors of 25 are all the positive or negative integers which divide the number 25 completely. So let us simply divide the number 25 by every number which completely divides 25 in ascending order till 25.
25 ÷ 1 = 25
25 ÷ 2 = not divides completely
25 ÷ 3 = not divides completely
25 ÷ 4 = not divide completely
25 ÷ 5 = 5
25 ÷ 6 = not divides completely
Similar numbers from 7 to 24 does not divides 25
25 ÷ 25 = 1
So all factors of 25: 1, 5, and 25.
We know that factors also include negative integers hence we can also have,
list of negative factors of 25: -1, -5, and -25.
All Factors of 25 can be Listed as Follows
Hence 25 have a total of 3 positive factors and 3 negative factors.
All Factor Pairs of 25
All Factor Pairs of 25 are combinations of two factors that when multiplied together give 25.
List of all the positive pair factors of 25
1 x 25 = 25; (1, 25)
5 x 5 = 25; (5, 5)
So (1, 25), and ( 5, 5), are the positive pair factors of 25
As we know that Factors of 25 include negative integers too.
List of all the negative pair factors of 25:
-1 x -25 = 25
-5 x -5 = 25
So (-1, -25), and ( -5, -5) are the negative pair factors of 25
Now we will study what is the prime factorization of 25.
What is The Prime Factorization of 25
According to the prime factor definition, we know that the prime factor of a number is the product of all the factors that are prime( a number that divides by itself and only one). Hence we can list the prime factors from the list of factors of 25.
Or the other way to find the prime factorization of 25 is by prime factorization or by factor tree.
Now let us study prime factors of 25 by division method.
Prime Factors of 25 by Division Method
To calculate the prime factors of 25 by division method, first, take the least prime number that is 2. Divide it by 2 until it is completely divisible by 2. If at a point it is not divisible by 2 take the next least prime number that is 3. Perform the same steps and move forward, till we get 1, as the quotient. Here is the stepwise method to calculate the prime factors of 25
Step 1: Divide 25 with 2
25 ÷ 2 = 12.5
As it is not divisible by 2 completely let us take next prime number 3
Step 2: Now divide 25 by 3
25 ÷ 3 = 8.33
It is also not divisible by 3. so let us check with other prime numbers.
Step 3: Now 25 is divisible by 5
25 ÷ 5 = 5
Step 4: Now 5 is again divisible by 5
5 ÷ 5 = 1
We get the quotient 1.
From the above steps, we get a prime factor of 25 as 5 x 5= 52
And also, common factors of 25 are 5 x 5
The number 25 is a composite number because 25 can be divided by 1, by itself, and by 5. 5 is a prime number so we cannot split it into more prime numbers, and hence the factor tree of 25 is incomplete. Here is the factor tree of 25.
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Solved Examples
Example 1: Write down the factors of 21.
Solution:
21 ÷ 1 = 21
21 ÷ 3 = 7
21 ÷ 7 = 3
21 ÷ 21 = 1
Therefore the factors of 16 are 1, 3, 7, and 21.
Example 2: Write down the factors of 71.
Solution:
71 ÷ 1 = 71
71 ÷ 71 = 1
71 is a prime number so it has only two factors 1 and the number itself. Therefore the factors of 71 are 1 and 71.
Quiz Time
Find the factors for 21
Find the factors for 46
Importance of Factors
Factors are an important chapter in Maths. Everything around us in our daily lives has to do with factors. Telling the time or knowing the proportion of ingredients that are needed in order to bake a cake, are done via the knowledge of Factors. Knowing how to divide a number into equal parts is done through factors. You also need factors to compare the prices of products when you go to a store. All students of Maths need to have a sound understanding of the chapter on Factors. Questions that come from Factors can be quite scoring if the students learn about them well and practice on a regular basis.
Does Vedantu have anything on Factors in Maths?
Vedantu has sufficient study material on Factors. Students need to log into Vedantu’s portal using their credentials so as to understand the topic and do sums on the same. It has relevant material on the importance of factors.
FAQs on Factors of 25
1. How to Calculate Factors of Large Numbers?
We can calculate factors of large numbers by the trial division method. We first try to divide the number by the smallest number such that it should completely divide the number. The result is again divided by the next number. This step is continued till we get the quotient as 1. At last, we will get all the factors of a given number. For example, let us factorize 100
100 ÷ 2 = 50; first factor is 2
100 ÷ 4 = 25;second factor is 4
100 ÷ 5 = 20;third factor is 5
100 ÷ 10 = 10;fourth factor is 10
100 ÷ 20 = 5;fifth factor is 20
100 ÷ 25 = 4;sixth factor is 25
100 ÷ 50 = 2;seventh factor is 50
100 ÷ 100 = 1;eighth factor is 100
So the factors of 100 are 2, 4, 5, 10, 20, 25, 50, and 100.
2. List the Important Facts of the Factors.
Important Facts of Factors
A factor of any number is its exact divisor i.e it divides the given number exactly.
1 is a common factor of every number.
Every factor of a number is always less than or equal to the original number.
The original number itself is the greatest factor.
3. What are the factors of 25?
Factors of 25 would be the numbers that we get if we multiply 25 with other numbers so as to get 25 such as 1, 25, and 5. The chapter on Factors that’s on Vedantu- Factors of 25 - Factor Pairs of 25 \ Prime Factors of 25 will shed more light on this. This page has explained what factors are and how to derive each number’s factors. The explanations are simple and to the point. All students can read from here and then understand the topic well. This page is ideal for referring before a Math test on the same.
4. Is 4 a factor of 25?
4 does not get divided by 25 completely and so, it isn’t a factor. 25 and its factors have been explained on Vedantu’s online tutoring platform if the students refer to Factors of 25 - Factor Pairs of 25 \u0026 Prime Factors of 25. This page has been created by expert maths teachers for the students so that they understand how factors and numbers work. All factors of 25 have been mentioned on the page so that students go through those and then understand how factors are formed. This page is great for clearing all doubts related to the chapter.
5. Which are the negative factors of 25?
Negative factors of 25 include -1, -5, and -25. All the positive and negative factors have been explained on Vedantu’s page so that students know which needs to be used. Two negatives make a positive in Maths and so, when two negative numbers are multiplied with each other, they form a positive number. Hence, -1, -5, and -25 are all factors of 25. This chapter needs to be understood well before the main exams so that the students do not commit any errors in the same. This chapter is available on Vedantu and goes by the name of Factors of 25 - Factor Pairs of 25 \u0026 Prime Factors of 25
6. How do students learn about the prime factorization of 25?
The prime factor of any number is the product of all the factors that are prime. The students need to read Factors of 25 - Factor Pairs of 25 \u0026 Prime Factors of 25 so as to understand better. The factors and the prime factors of 25 can be understood once the students have read from here. It is an important topic in Maths that needs to be understood well so that the basics are logged into the student’s mind at an early age. The other important chapters in Maths will also be based on this. This page is available on Vedantu’s portal and is completely free of cost.
7. Where can students find some solved examples on factors in Maths?
Certain solved examples on factors have been given on Factors of 25 - Factor Pairs of 25 / Prime Factors of 25. Solved examples teach the students the manner of tackling difficult problems. They need to practice from them well so as to get a complete understanding of the chapter. They also help the student assess his/ her math skills as going through solved sums will enlighten them about the approach that needs to be used while solving problems. Factors and its sums can be understood if the students read from here.
