Factors of 25 Using Prime Factorization
What are the Factors of 25?
If the number 25 is divided by a positive integer such that the remainder is zero, the integer is known as a factor of 25. Here, the quotient obtained on division is also a factor of 25.
The factors of 25 are 1, 5, and 25 because all these numbers divide the number 25 evenly.
Deriving Factor List of 25
Divisor | Is the number a factor of 25? | Multiplication equation |
|---|---|---|
1 | Yes, 1 is a factor of every number. | 1 x 25 = 25 |
2 | No, 25 is not even. | - |
3 | No, 2 + 5 = 7, 7 is not divisible by 3. | - |
4 | No, 25 \(\div\) 4 = 6R1 | - |
5 | Yes, ones digit is 5. | 5 x 5 = 25 |
6 | No, 25 is not even nor is it divisible by 3. | - |
7 | No, 25 \(\div\) 7 = 3R4 | - |
8 | No, 25 \(\div\) 8 = 3R1 | - |
9 | No, 25 \(\div\) 9 = 2R7 | - |
The Prime Factorization of 25
25 is a composite number having factors other than 1 and itself. The process of expressing a composite number as a product of its prime factors is known as prime factorization.
The factor tree of 25 can be written as:
So, the prime factorization of 25 is 25 = 5 x 5 or 5\(^2\).
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The Factor Pairs of 25
The factor pairs of 25 are the pairs of prime numbers that when multiplied result in 25.
1 x 25 = 25
5 x 5 = 25
Hence, the factor pairs of 25 are (1, 25) and (5, 5).
Solved Factors of 25 Examples
Example 1: Find the common factors of 20 and 25.
Solution:
The factors of 20 = 1, 2, 4, 5, 10, and 20
The factors of 25 = 1, 5, and 25
Therefore, the common factors of 20 and 25 are 1 and 5.
Example 2: Find the greatest common factor of 25 and 36.
Solution:
The factors of 25 = 1, 5, and 25
The factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, and 36
The only common factor of 25 and 36 is 1.
So, the greatest common factor of 25 and 36 is also 1.
Example 3: Ray has 25 liters of milk. He wishes to divide it equally among the 6 of his cats. Can he do so?
Solution:
\(\frac{25}{6}\) = 4R1. Hence, 6 is not a factor of 25 because when 25 is divided by 6, we get a remainder of 1.
So, he cannot divide 25 liters of milk equally among the 6 cats. However, what he can do is, give 4 liters of milk to each cat. Then he would be left with 1 liter of milk.
The factor pairs of 25 are the pairs of numbers whose product is 25. The factor pairs of 25 are (1, 25) and (5, 5).
If we divide 25 by 16, we get the remainder as 9. So, 16 is not a factor of 25.
The factors of 25 are 1, 5, and 25. Both 1 and 25 are not prime numbers. Hence, 5 is the only prime factor of 25.
The prime factorization of 25 is 5 x 5 or 5\(^2\). So, we can see that the base is 5 and the exponent of 5 is 2.