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Factors of 25 are those numbers that divide 25 exactly without leaving any remainder. The numbers that give 25 as a result when multiplied together in a pair of two are the factors of 25. 1, 5, and 25 are the three factors of 25. 5 is the smallest factor of 25 whereas 25 itself is the biggest factor of 25. The sum of the factors of 25 is 31. The prime factorization of 25 is 5 × 5 and thus there is only one prime factor of 25 which is 5. The pair factors of 25 are (1, 25) and (5, 5) which can be represented in both positive and negative forms. The pair factor of 25 can be (1, 25) or (-1, -25).
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Key Terms: Factors of 25, Remainder, Prime Factorization, Factors, Pair Factors, Multiplication, Prime Factor, Prime Number
What are Factors of 25?
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Factors of 25 are those numbers that give the value 25 on multiplication in pairs. They are the numbers that leave zero as the remainder on dividing 25. 25 is an odd composite number, which means it has more than two factors.25 has a total of 3 factors which are. 1, 5, and 25. The negative factors of 25 are -1, -5, and -25.
Factors of 25: 1, 5, 25
Factors of 25
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Pair Factors of 25
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The pair factor of 25 refers to the pair of two numbers, which on multiplication results in an original number 25. The pair factors of 25 can be in positive as well as a negative form. It is possible for a number to have negative pair factors as well because the product of two negative numbers is also a positive number.
- The positive pair factors of 25 include (1, 25) and (5, 5).
- The negative pair factors of 25 include (-1, -25) and (-5, -5).
Prime Factorization of 25
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Prime Factorization refers to the expression of a composite number as the product of its prime factors. 25 is a composite number which means it has more than 2 factors.
Prime Factorization of 25
Step 1: First we will divide the number 25 by the smallest prime factor 2.
25 ÷ 2 = 12.5
Thus, 2 cannot be a prime factor of 25.
Step 2: Proceeding with the next prime number 3
25 ÷ 3 = 8.33
Thus, 3 cannot be a prime factor of 25.
Step 3: Moving on to the next prime number, 5, and divide it till we get a 1 as the output.
25 ÷ 5 = 5
5 ÷ 5 = 1
We can see that we get 1 at the end of the division process and we cannot factorize it further.
Thus, the prime factorization of 25 is 5 × 5 or 52. 5 is the only prime factor of 25.
Factors of 25 by Division Method
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In order to find out the factors of 25, we need to find out all those numbers that divide 25 without leaving any remainder. Beginning with the number 1, we will move to the number 25.
- The numbers that divide 25 completely with no remainder are the factors of 25.
- The numbers that do not divide 25 completely and leave a remainder are not the factors of 25.
The division of 25 by its factors is as follows:
- 25 ÷ 1 = 25 (Remainder = 0, Factor = 1)
- 25 ÷ 5 = 5 (Remainder = 0, Factor = 5)
- 25 ÷ 25 = 1 (Remainder = 0, Factor = 25)
Thus, there are only three factors of 25 which are 1, 5 and 25. If we divide 25 by any number other than 1, 5, and 25, it will leave a remainder, and hence they are not the factors of 25.
Read More: Greatest Common Divisor
Solved Examples on Factors of 25
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Example 1: List down the common factors of 25 and 24.
Solution: First we will write down all the factors of 25 and 24.
- Factors of 25: 1, 5, and 25
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, and 24
Thus, we can see that there is only one common factor of 25 and 24 which is 1.
Example 2: Find the common factors of 25 and 30.
Solution: Writing down all the factors of 15 and 30,
- Factors of 25: 1, 5, and 25
- Factors of 26: 1, 2, 3, 5, 6, 10, 15, and 30
Hence, the common factor of 25 and 30 are 1 and 5.
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| Addition and Subtraction of Integers | Relation Between HCF and LCM | Properties of LCM and HCF |
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Things to Remember
- Factors of 25 are the numbers that divide 25 completely leaving zero as the remainder.
- The factors of 25 are 1, 5, and 25.
- The pair factors of 25 give the value 25 on multiplication with each other.
- The prime factorization of 25 is 5 x 5 = 52.
- There is only one prime factor of 25 which is 5.
- The sum of all three factors of 5 is 31.
Sample Questions
Ques. List the factors of 25 and 26 and mention their common factors. (2 Marks)
Ans. The factors of 25 and 26 are
- Factors of 25 = 1, 5, 25
- Factors of 26 = 1, 2, 13, 26
There is only one common factor of 25 and 26 which is 1.
Ques. Write down all the factors of 25 and 13. What is the common factor of both numbers? (2 Marks)
Ans. The factors of 25 and 13 are as follows:
- Factors of 25 =1, 5, and 25
- Factors of 13 = 1 and 13
The common factor of 25 and 13 is only 1.
Ques. List the pair factors of 25. (2 Marks)
Ans. The pair factors of 25 are as follows:
- Positive pair factors of 25: (1, 25) and (5, 5)
- Negative factors of 25: (-1, -25) and (-5, -5)
Ques. Rahil throws his birthday party at his house. He invited 25 friends from his class to the party. He wants to divide them into groups for a game. How will he arrange so that no child is left out? (3 Marks)
Ans. Here we will use the concept of factors of 25 as there are total 25 children.
The factors of 25 are 1, 5, and 25, thus, the children can be arranged only in one way which is by dividing 25 by its factor 5.
25 ÷ 5 = 5
Thus, there would be 5 groups with 5 children each.
Ques. Here are a few numbers- 1, 5, 6, 8, 9, 25. Find the number which is not included in the factors of 25. (2 Marks)
Ans. The numbers that divide 25 completely are the factors of 25, so
1, 5, and 25 are the factors of 25 but when we divide 25 by 6, 8, and 9, it leaves a reminder.
As a result,1, 5, and 25 are factors of 25 but 6, 8, and 9 are not the factors of 25.
Ques. How many prime factors does 25 have? (1 Mark)
Ans. 25 has only one prime factor which is 5.
Ques. List the Greatest Common Factor of 25 and 14. (2 Marks)
Ans. To find the greatest common factor of 25 and 14, we first need to know the factors of both of them,
- Factors of 25: 1, 5, 25
- Factors of 14: 1, 2, 7, 14.
There is only one common factor of 25 and 14 which is 1, thus, the Greatest Common Factor (GCF) of 25 and 14 is 1.
Ques. Is 4 a factor of 25 or not? Give reason. (1 Mark)
Ans. To find out whether 4 is a factor of 25 or not, we need to divide 25 by 4.
25 ÷ 4 = 6.25
Thus, 4 is not a factor of 25 as it leaves a remainder.
Ques. Write down the prime factorization of 25. (1 Mark)
Ans. The prime factorization of 25 is 5 × 5. It can also be written as 52.
Ques. How many factors does 25 have? What is the sum of them? (2 Marks)
Ans. There are 3 factors of 25- 1, 5 and 25.
The sum of the factors of 25 is as follows:
1 + 5 + 25 = 31
Thus, the sum of all the three factors of 25 is 31.
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