Factors of 25 are 1, 5, 25. Including 1 and 25 itself, there are 3 distinct factors for 25.
The prime factors of 25 are 5, and its factor pairs are (1, 25), (5, 5). We've put this below in a table for easy sharing.
| Factors of 25: | 1, 5, 25 |
| Prime Factors of 25: | 5 |
| Factor Pairs of 25: | (1, 25), (5, 5) |
How to calculate factors?
To be a factor of 25, a number must divide 25 exactly, leaving no remainder. In other words, when 25 is divided by this number, the quotient is a whole number. These factors, also known as divisors, define the structure of 25 and are key in understanding its mathematical properties.
Below, we outline how to calculate the factorization of 25 using four methods: basic factorization, prime factorization, the division method, or using GCD and LCM. We also include a detailed analysis of factor pairs and a factor tree to illustrate the breakdown.
Method 1: Basic Factorization
Basic Factorization is a method to find the factors of a number by systematically testing each whole number from 2 up to the number itself to see which ones divides with zero remainder (evenly). The process is somewhat time consuming if a number is high, that's why you should master divisibility rules, to make the process faster.
Here's the breakdown for 25:
| Divisor | Is it a factor of 25? | Verification |
|---|---|---|
| 1 | Yes, 1 is a factor of every number. | 1 × 25 = 25 |
| 2 | No, 25 is not an even number so it's not divisible by 2. | - |
| 3 | No, the sum of its digits (7) is not divisible by 3. | - |
| 4 | No, the last two digits (25) do not form a number divisible by 4. | - |
| 5 | Yes, 25 ends with 0 or 5, so it's divisible by 5. | 5 × 5 = 25 |
| 6 | No, 25 is not divisible by both 2 and 3. | - |
| 7 | No, 25 divided by 7 leaves a remainder of 4. | - |
| 8 | No, the last three digits (25) do not form a number divisible by 8. | - |
| 9 | No, the sum of its digits (7) is not divisible by 9. | - |
| 10 | No, last digit is 5, so not divisible by 10. | - |
| 11 | No, the difference between sums of alternating digits (3) is not divisible by 11. | - |
| 12 | No, 25 is not divisible by both 3 and 4. | - |
| ... | continue with all the other numbers. |
Method 2: Prime Factorization
Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. This means a prime number cannot be formed by multiplying two smaller natural numbers. For example:
- 2 is a prime number because its only divisors are 1 and 2.
- 3 is prime for the same reason—it can only be divided evenly by 1 and 3.
- 4 is not prime because it can be divided by 1, 2, and 4.
- 5, 7, 11, and 13 are also prime numbers.
Prime numbers are fundamental in mathematics because they are the "building blocks" of whole numbers. Any natural number greater than 1 can be expressed as a product of prime numbers, which is known as its prime factorization.
How to do prime factorization of 25
You start by dividing 25 to each prime number, multiple times, until the remainder is 0. Then you move on to the next prime number. To save time, you should test with up to \( \sqrt25 \)
| Prime Number | Is it a factor of 25? | Verification |
|---|---|---|
| 2 | No, 25 is not divisible by 2. | - |
| 3 | No, 25 is not divisible by 3. | - |
| 5 | Yes, 25 is divisible by 5. | 25 ÷ 5 = 5, R0 |
| 5 | Yes, the result 5 is divisible by 5. | 5 ÷ 5 = 1, R0 |
Method 3: Division Method
The Division Method is a systematic approach to finding all the factors of a 25 by performing successive divisions. This method involves dividing 25 by every integer from 1 up to 25 and identifying the numbers that divide exactly without leaving a remainder. In the table below we've ommitted the numbers that don't divide 25, and only kept those that do:
| Divisor | Verification |
|---|---|
| 1 | 25 ÷ 1 = 25 |
| 5 | 25 ÷ 5 = 5 |
| 25 | 25 ÷ 25 = 1 |
Using the division method, we calculated that factors of 25 are 1, 5, 25.
Factor Tree of 25
The factor tree of 25 shows the step-by-step breakdown of 25 into its prime factors. Each branch of the tree represents a division of 25 into two factors until all resulting factors are prime numbers. This visual representation helps identify the building blocks of 25 and highlights the structure of its prime factorization.
| 25 | |
| | | \ |
| 5 | 5 |
Factor Pairs of 25 (Visualization)
Factor pairs of 25 are sets of two numbers that, when multiplied together, result in 25. Factor pairs are symmetric and mirror around the square root of 25, such as (1, 25) and (25, 1), and can be both positive and negative pairs as long as their product equals 25.
| Negative factor pairs | Positive factor pairs |
|---|---|
| (-1, -25) | (1, 25) |
| (-5, -5) | (5, 5) |
All factor pairs of 25 are (1, 25), (5, 5), (-1, -25), (-5, -5).
Why Should I Care About Factors of 25?
Turns out, factors aren’t just about boring math equations—they’re like secret superpowers hiding inside numbers! Knowing them can help you split things up, share with friends, or even spot hidden patterns. Want to know how? Check out these real-life examples that show just how cool factors really are:
- Arranging Desks: You have 25 desks and want to arrange them into equal rows. If each row has 5 desks, you’ll create 5 rows because 5 × 5 = 25.
- Creating Rows: You have 25 items to display. If you arrange them into 1 rows, there will be 25 items in each row because 1 × 25 = 25.
- Distributing Posters: You have 25 posters to distribute. If each store takes 1 posters, you can deliver to 25 stores because 1 × 25 = 25.
- Planting Flowers: You have 25 flower seeds to plant in a garden. If each row contains 5 seeds, you’ll plant 5 rows because 5 × 5 = 25.
- Packing Snacks: You have 25 snack packs to prepare for a trip. If each person needs 1 snack packs, you’ll prepare enough for 25 people because 1 × 25 = 25.