Factors of 25 are the numbers, which gives the result as 25 when multiplied together in pair of two. When we divide a number by one of its factors, then the resultant quotient is a whole number. The factors of 25 can be represented in positive as well as in negative form, but it cannot be a decimal or fraction. Similarly, the pair factors of 25 can also be represented in positive and negative form. For example, the pair factor of 25 can be (1, 25) or (-1, -25). If we multiply a pair of negative numbers, such as multiplying -1 and -5, it will result in 25. In this article, we will learn the factors of 25, and how to find the factors of 25 using the division method and the pair factors and the prime factors of 25 using the prime factorization method.
Table of Contents:
- What are the Factors of 25?
- Pair Factors of 25
- Factors of 25 by Division Method
- Prime Factorization of 25
- Solved Examples
- FAQs
What are the Factors of 25?
The factors of 25 are the numbers that divide 25 exactly without leaving any remainder. As 25 is a composite number, it has many factors other than 1 and 25. Thus, the factors of 25 are 1, 5 and 25. Similarly, the negative factors of 25 are -1, -5 and -25.
Factors of 25: 1, 5 and 25. Prime Factorization of 25: 5 × 5 or 5^{2}. |
Pair Factors of 25
The pair factor of 25 is a pair of numbers, which on multiplication results in an original number. As discussed above, the pair factors of 25 can be in positive or negative form. Thus, the positive and negative pair factors of 25 are given below:
Positive Pair Factors of 25:
Positive Factors of 25 |
Positive Pair Factors of 25 |
1 × 25 |
(1, 25) |
5 × 5 |
(5, 5) |
Negative Pair Factors of 25:
Negative Factors of 25 |
Negative Pair Factors of 25 |
-1 × -25 |
(-1, -25) |
-5 × -5 |
(-5, -5) |
Factors of 25 by Division Method
The factors of 25 can be easily found using the division method. In this method, 25 is divided by different integers. If the integers divide 25 exactly and leave the remainder 0, then those integers are considered as the factors of 25. Now, let us discuss how to find the factors of 25 using the division method.
- 25/1 = 25 (Factor is 1 and Remainder is 0)
- 25/5 = 5 (Factor is 5 and Remainder is 0)
- 25/25 = 1 (Factor is 25 and Remainder is 0)
Thus, the factors of 25 are 1, 5 and 25.
Note: If we divide 25 by any numbers other than 1, 5 and 25, it leaves a remainder 0, and hence they are not the factors of 25.
Prime Factorization of 25
The number 25 is a composite number. Now let us find the prime factors of 25.
- The first step is to divide the number 25 with the smallest prime factor,i.e. 2
25 ÷ 2 = 12.5
Therefore, 2 cannot be a prime factor of 25.
- Now, proceed to the next prime numbers, i.e. 3
25 ÷ 3 = 8.33
Therefore, 3 cannot be a prime factor of 25.
- Again, moving to the next prime number, 5 and continue dividing till you get a fraction or 1 as the output.
25 ÷ 5 = 5
5 ÷ 5 = 1
- We have received 1 at the end of the division process and further, we cannot proceed. So, the prime factors of 25 are 5 × 5 or 5^{2}, where 5 is a prime number.
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Examples
Example 1:
Find the factors of 25 and 24.
Solution:
The factors of 25 are 1, 5 and 25.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
Thus, the common factor of 25 and 24 is 1.
Example 2:
Find the factors of 25 and 26.
Solution:
Factors of 25 = 1, 5 and 25.
Factors of 26 = 1, 2, 13 and 26.
Hence, the common factor of 25 and 26 is 1.
Example 3:
Find the factors of 25 and 13.
Solution:
The factors of 25 are 1, 5 and 25.
The factors of 13 are 1 and 13.
As 13 is a prime number, the common factor of 25 and 13 is 1.
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Frequently Asked Questions on Factors of 25
What are the factors of 25?
The factors of 25 are 1, 5 and 25 and its negative factors are -1, -5 and -25.
What is the prime factorization of 25?
The prime factorization of 25 is 5 × 5 or 5^{2}.
What are the positive and negative factors of 25?
The positive factors of 25 are (1, 25) and (5, 5)
The negative factors of 25 are (-1, -25) and (-5, -5)
What is the sum of factors of 25?
The sum of factors of 25 is 31. We know that the factors of 25 are 1, 5 and 25.
Hence, the sum of factors of 25 = 1+5+25 = 31.
Is 4 a factor of 25?
No, 4 is not a factor of 25. If 4 divides 25, it leaves a remainder, and hence 4 is not a factor of 25.