If a number completely divides 25 without leaving a remainder, then that number is called a factor of 25. So we can say that the factors of 25 are the divisors of 25. In this section, we will learn about the factors of 25 and the prime factors of 25.
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Table of Contents
Highlights of Factors of 25
- 25=5×5 is the prime factorization of 25.
- The factors of 25 are 1, 5, and 25.
- The only prime factor of 25 is 5.
- Negative factors of 25 are -1, -5, and -25.
What are the factors of 25?
By the multiplication method, we will first find the factors of 25. Let us write the number 25 multiplicatively in all possible ways. We definitely have:
| 25 = 1×25 | ∴ 1, 25 are factors of 25 |
| 25 = 5×5 | ∴ 5 is a factor of 25 |
We cannot write 25 multiplicatively in any other way than the above ones, so we will stop right now. Note that the factors of 25 are the numbers in brown color.
So the factors of 25 are 1, 5, and 25.
We know that m is a factor of 25 if and only if -m is a factor of 25. So the negative factors of 25 are -1, -5, and -25.
Pair Factors of 25
| 25 = a×b | Factors in Pairs (a,b) |
| 25 = 1×25 | (1, 25) |
| 25 = 5×5 | (5, 5) |
Thus the pair factors of 25 are (1, 25) and (5, 5).
We know that if (a, b) is a positive pair factor of 25, then (-a, -b) is a negative pair factor of 25. Thus, all the negative pair factors of 25 are (-1, -25) and (-5, -5).
Number of factors of 25
From above we have calculated the factors of 25 which are 1, 5, and 25. Thus the total number of factors of 25 is three.
Prime Factors of 25
Note that the factors of 25 are 1, 5, and 25. Among those factors, we observe that only 5 is a prime number as 5 does not have any proper divisors.
∴ the only prime factor of 25 is 5.
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| Factors of 55: | 1, 5, 11, 55 |
| Factors of 42: | 1, 2, 3, 6, 7, 14, 21, 42 |
| Factors of 38: | 1, 2, 19, 38 |
| Factors of 56: | 1, 2, 4, 7, 8, 14, 28, 56 |
Question: What are the factors of 25?
Video Solution:
Factors of -25
The factors of negative 25 include both the positive and negative factors of 25. They are 1, -1, 5, -5, 25, and -25.
How to find factors of 25?
Now we will determine the factors of 25 by division method. In this method, we will try to find the numbers that can divide 25 with no remainder. See that
| 25/1=25 and the remainder is 0 | ∴ 1 and 25 are factors of 25 |
| 25/5=5 and the remainder is 0 | ∴ 5 is a factor of 25 |
Note that no numbers other than the numbers in violet color can divide 25. So the numbers in violet color, that is, 1, 5, and 25 are the complete list of factors of 25.
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