Factors of 25 are the list of integers that we can split evenly into 25. There are overall 3 factors of 25 among which 25 is the biggest factor and 1, 5, and 25 are positive factors. The sum of all factors of 25 is 31. Its Prime Factors are 1, 5, 25, and (1, 25) and (5, 5) are Pair Factors.
- Factors of 25: 1, 5 and 25
- Negative Factors of 25: -1, -5 and -25
- Prime Factors of 25: 5
- Prime Factorization of 25: 5 × 5 = 52
- Sum of Factors of 25: 31
| 1. | What are Factors of 25? |
| 2. | How to Calculate Factors of 25? |
| 3. | Factors of 25 by Prime Factorization |
| 4. | Thinking Out of The Box! |
| 5. | Factors of 25 in Pairs |
| 6. | Important Notes |
| 7. | FAQs on Factors of 25 |
What are Factors of 25?
Factors of 25 are all the numbers which, on multiplying, give the value 25. As 25 is odd, it will not have 2 or any multiples of 2 as its factor. To understand why it is composite, let's recall the definition of a composite number. A number is said to be composite if it has more than two factors. In this case, 25 has a total of 3 factors i.e. 1, 5, and 25.
How to Calculate the Factors of 25?
To calculate the factors of any number, here in this case 25, we need to find all the numbers that would divide 25 without leaving any remainder. We start with the number 1, then check for numbers 2, 3, 4, 5, 6, 7, etc. up to 25 respectively. The number 1 and the number itself would always be a factor of the given number.
Refer to the following table to check the division of 25 by its factors:
| Division | Factor |
|---|---|
| 25/1 | Remainder = 0 |
| 25/5 | Remainder = 0 |
| 25/25 | Remainder = 0 |
Hence, factors of 25 are 1, 5, and 25. Explore factors using illustrations and interactive examples:
- Factors of 125- The factors of 125 are 1, 5, 25, 125
- Factors of 225- The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225
- Factors of 256 - The factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, and 256
- Factors of 625 - The factors of 625 are 1, 5, 25, 125, and 625
- Factors of 250 - The factors of 250 are 1, 2, 5, 10, 25, 50, 125, and 250
Factors of 25 by Prime Factorization
Prime factorization means expressing a composite number as the product of its prime factors. To get the prime factorization of 25, we divide it by its smallest prime factor, which is 5.
- 25 ÷ 5 = 5
Now divide 5 by its smallest prime factor and continue this process till we get the quotient as 1. The prime factorization of 25 is shown below:
So, the prime factorization of 25 is:
- 5 × 5 = 25 or 25 = 52
So the number 25 can be called a perfect square. The factors of 25 are 1, 5, and 25. (The only prime factor is 5.)
Think Tank:
- Determine a number other than 25, which has only three factors and is a perfect square.
- Determine the common factors of 25 and 50.
Factors of 25 in Pairs
Let's write factors of 25 in pairs. The pair factors of 25 can be given as below:
- (1, 25) ; (5, 5)
These factors given above are positive pair factors. It is possible to have negative pair factors as well because the product of two negative numbers is also a positive number. Let's have a look at negative pair factors:
- (-1, -25) ; (-5, -5)
Important Notes:
- As 25 is an odd number, all of its factors will also be odd.
- 25 is a perfect square number.
- Factors are never fractions or decimals
Factors of 25 Solved Examples
Example 1:
Mr. William plans for an interactive activity for the children of his class on the occasion of Christmas.
There are 25 children in all. He wants to put them in small groups having equal numbers so that no child is left. In how many ways can he arrange them?
Solution:
The factors of 25 are 1, 5, and 25. So the children can be arranged only in one way.
That is 5 children in each group and 5 groups in all.
Example 2:
Silvia takes out a set of 25 soup bowls to be stacked on the dining table. In how many ways can she stack them?
Solution:
To solve this problem, we need to know the factors of 25. List them out: 1, 5, and 25, therefore the factor pairs are: (1,25), (5,5).
The first pair, 1 and 25, doesn't tell us much. It just means that we could have 1 stack of 25 soup bowls.
The second pair tells us we could have 5 stacks of 5 soup bowls.
Example 3: Kevin was asked to find the factors of 25 and 30. What will be his answer?
Solution:
Factors of 25 are 1, 5, and 25. Similarly, the factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 3
Example 4: Few numbers were given to Sam and he was asked to find the number which is not a factor of 25. Help Sam find that number.
1, 5, 6, 8, 9, 25
Solution:
The factors of 25 are 1, 5, and 25 but when we divide 25 by 6, 8, and 9, it leaves a reminder.
Therefore 1, 5, and 25 are factors of 25 but 6, 8, and 9 are not the factors of 25.
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FAQs on Factors of 25
What are the Factors of 25?
The factors of 25 are 1, 5, 25 and its negative factors are -1, -5, -25.
What Numbers Are the Prime Factors of 25?
The prime factor of 25 is 5.
What is the Sum of the Factors of 25?
All the Factors of 25 are 1, 5, 25 and therefore the sum of all these factors is 1 + 5 + 25 = 31
How Many Factors of 25 are also Factors of 9?
Since, the factors of 25 are 1, 5, 25, and factors of 9 are 1, 3, 9. Hence, 25 and 9 have only one common factor which is 1. Therefore, 25 and 9 are co-prime.
What is the Greatest Common Factor of 25 and 14?
The factors of 25 are 1, 5, 25 and the factors of 14 are 1, 2, 7, 14. 25 and 14 have only one common factor which is 1. This implies that 25 and 14 are co-prime.
Hence, the Greatest Common Factor (GCF) of 25 and 14 is 1.
