Factors of 10 are 1, 2, 5, 10. Including 1 and 10 itself, there are 4 distinct factors for 10.
The prime factors of 10 are 2, 5, and its factor pairs are (1, 10), (2, 5). We've put this below in a table for easy sharing.
| Factors of 10: | 1, 2, 5, 10 |
| Prime Factors of 10: | 2, 5 |
| Factor Pairs of 10: | (1, 10), (2, 5) |
How to calculate factors?
To be a factor of 10, a number must divide 10 exactly, leaving no remainder. In other words, when 10 is divided by this number, the quotient is a whole number. These factors, also known as divisors, define the structure of 10 and are key in understanding its mathematical properties.
Below, we outline how to calculate the factorization of 10 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 10:
| Divisor | Is it a factor of 10? | Verification |
|---|---|---|
| 1 | Yes, 1 is a factor of every number. | 1 × 10 = 10 |
| 2 | Yes, 10 is an even number so it's divisible by 2. | 2 × 5 = 10 |
| 3 | No, the sum of its digits (1) is not divisible by 3. | - |
| 4 | No, the last two digits (10) do not form a number divisible by 4. | - |
| 5 | Yes, 10 ends with 0 or 5, so it's divisible by 5. | 5 × 2 = 10 |
| 6 | No, 10 is not divisible by both 2 and 3. | - |
| 7 | No, 10 divided by 7 leaves a remainder of 3. | - |
| 8 | No, the last three digits (10) do not form a number divisible by 8. | - |
| 9 | No, the sum of its digits (1) is not divisible by 9. | - |
| 10 | Yes, 10 ends with 0, so it's divisible by 10. | 10 × 1 = 10 |
| ... | 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 10
You start by dividing 10 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 \( \sqrt10 \)
| Prime Number | Is it a factor of 10? | Verification |
|---|---|---|
| 2 | Yes, 10 is divisible by 2. | 10 ÷ 2 = 5, R0 |
| 2 | No, the result 5 is not divisible by 2. | - |
| 5 | 5 is a prime number. | 5 is prime. |
Method 3: Division Method
The Division Method is a systematic approach to finding all the factors of a 10 by performing successive divisions. This method involves dividing 10 by every integer from 1 up to 10 and identifying the numbers that divide exactly without leaving a remainder. In the table below we've ommitted the numbers that don't divide 10, and only kept those that do:
| Divisor | Verification |
|---|---|
| 1 | 10 ÷ 1 = 10 |
| 2 | 10 ÷ 2 = 5 |
| 5 | 10 ÷ 5 = 2 |
| 10 | 10 ÷ 10 = 1 |
Using the division method, we calculated that factors of 10 are 1, 2, 5, 10.
Factor Tree of 10
The factor tree of 10 shows the step-by-step breakdown of 10 into its prime factors. Each branch of the tree represents a division of 10 into two factors until all resulting factors are prime numbers. This visual representation helps identify the building blocks of 10 and highlights the structure of its prime factorization.
| 10 | |
| | | \ |
| 2 | 5 |
Factor Pairs of 10 (Visualization)
Factor pairs of 10 are sets of two numbers that, when multiplied together, result in 10. Factor pairs are symmetric and mirror around the square root of 10, such as (1, 10) and (10, 1), and can be both positive and negative pairs as long as their product equals 10.
| Negative factor pairs | Positive factor pairs |
|---|---|
| (-1, -10) | (1, 10) |
| (-2, -5) | (2, 5) |
All factor pairs of 10 are (1, 10), (2, 5), (-1, -10), (-2, -5).
Why Should I Care About Factors of 10?
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:
- Distributing Flyers: You have 10 flyers to distribute. If you give each person 2 flyers, you will need 5 people to help because 2 × 5 = 10.
- Baking Cookies: You baked 10 cookies and want to pack them in boxes. If each box holds 2 cookies, you’ll need 5 boxes because 2 × 5 = 10.
- Watering Plants: You have 10 plants that need watering. If each watering can waters 1 plants, you’ll need 10 cans to water them all because 1 × 10 = 10.
- Handing Out Balloons: You have 10 balloons to hand out at a party. If each guest receives 1 balloons, you’ll have enough for 10 guests because 1 × 10 = 10.
- Organizing a Classroom: You have 10 students in a class. If you arrange them into groups of 1, you’ll create 10 groups because 1 × 10 = 10.
