Factors of 25 With Examples
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.
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 Twenty Five
The pair factor of Twenty Five 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 Twenty Five are given below:
Positive Pair Factors of Twenty Five:
Positive Factors of Twenty Five |
Positive Pair Factors of Twenty Five |
1 × 25 |
(1, 25) |
5 × 5 |
(5, 5) |
Negative Pair Factors of Twenty Five:
Negative Factors of Twenty Five |
Negative Pair Factors of Twenty Five |
-1 × -25 |
(-1, -25) |
-5 × -5 |
(-5, -5) |
Factors of Twenty Five by Division Method
The factors of Twenty Five 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 Twenty Five. Now, let us discuss how to find the factors of Twenty Five 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 Twenty Five 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 Twenty Five.
Prime Factorization of 25
The number 25 is a composite number. Now let us find the prime factors of Twenty Five.
- 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 Twenty Five are 5 × 5 or 5^{2}, where 5 is a prime number.
Examples
Example 1:
Find the factors of Twenty Five 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 Twenty Five and 24 is 1.
Example 2:
Find the factors of Twenty Five and 26.
Solution:
Factors of Twenty Five = 1, 5 and 25.
Factors of 26 = 1, 2, 13 and 26.
Hence, the common factor of 25 and 26 is 1.
Frequently Asked Questions on Factors of Twenty Five
Q1 What are the factors of Twenty Five?
Ans. The factors of Twenty Five are 1, 5 and 25 and its negative factors are -1, -5 and -25.
Q2 What is the prime factorization of Twenty Five?
Ans. The prime factorization of 25 is 5 × 5 or 5^{2}.
Q3 What are the positive and negative factors of Twenty Five?
Ans. The positive factors of Twenty Five are (1, 25) and (5, 5)
The negative factors of 25 are (-1, -25) and (-5, -5)
Q4 What is the sum of factors of Twenty Five?
Ans. The sum of factors of Twenty Five is 31. We know that the factors of 25 are 1, 5 and 25.
Hence, the sum of factors of Twenty Five = 1+5+25 = 31.
Q5 Is 4 a factor of Twenty Five?
Ans. No, 4 is not a factor of Twenty Five. If 4 divides 25, it leaves a remainder, and hence 4 is not a factor of Twenty Five.
Category: Maths