Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. Including 1 and 100 itself, there are 9 distinct factors for 100.
The prime factors of 100 are 2, 5, and its factor pairs are (1, 100), (2, 50), (4, 25), (5, 20), (10, 10). We've put this below in a table for easy sharing.
| Factors of 100: | 1, 2, 4, 5, 10, 20, 25, 50, 100 |
| Prime Factors of 100: | 2, 5 |
| Factor Pairs of 100: | (1, 100), (2, 50), (4, 25), (5, 20), (10, 10) |
How to calculate factors?
To be a factor of 100, a number must divide 100 exactly, leaving no remainder. In other words, when 100 is divided by this number, the quotient is a whole number. These factors, also known as divisors, define the structure of 100 and are key in understanding its mathematical properties.
Below, we outline how to calculate the factorization of 100 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 100:
| Divisor | Is it a factor of 100? | Verification |
|---|---|---|
| 1 | Yes, 1 is a factor of every number. | 1 × 100 = 100 |
| 2 | Yes, 100 is an even number so it's divisible by 2. | 2 × 50 = 100 |
| 3 | No, the sum of its digits (1) is not divisible by 3. | - |
| 4 | Yes, the last two digits (0) form a number divisible by 4. | 4 × 25 = 100 |
| 5 | Yes, 100 ends with 0 or 5, so it's divisible by 5. | 5 × 20 = 100 |
| 6 | No, 100 is not divisible by both 2 and 3. | - |
| 7 | No, 100 divided by 7 leaves a remainder of 2. | - |
| 8 | No, the last three digits (100) do not form a number divisible by 8. | - |
| 9 | No, the sum of its digits (1) is not divisible by 9. | - |
| 10 | Yes, 100 ends with 0, so it's divisible by 10. | 10 × 10 = 100 |
| 11 | No, the difference between sums of alternating digits (1) is not divisible by 11. | - |
| 12 | No, 100 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 100
You start by dividing 100 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 \( \sqrt100 \)
| Prime Number | Is it a factor of 100? | Verification |
|---|---|---|
| 2 | Yes, 100 is divisible by 2. | 100 ÷ 2 = 50, R0 |
| 2 | Yes, the result 50 is divisible by 2. | 50 ÷ 2 = 25, R0 |
| 2 | No, the result 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 100 by performing successive divisions. This method involves dividing 100 by every integer from 1 up to 100 and identifying the numbers that divide exactly without leaving a remainder. In the table below we've ommitted the numbers that don't divide 100, and only kept those that do:
| Divisor | Verification |
|---|---|
| 1 | 100 ÷ 1 = 100 |
| 2 | 100 ÷ 2 = 50 |
| 4 | 100 ÷ 4 = 25 |
| 5 | 100 ÷ 5 = 20 |
| 10 | 100 ÷ 10 = 10 |
| 20 | 100 ÷ 20 = 5 |
| 25 | 100 ÷ 25 = 4 |
| 50 | 100 ÷ 50 = 2 |
| 100 | 100 ÷ 100 = 1 |
Using the division method, we calculated that factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100.
Factor Tree of 100
The factor tree of 100 shows the step-by-step breakdown of 100 into its prime factors. Each branch of the tree represents a division of 100 into two factors until all resulting factors are prime numbers. This visual representation helps identify the building blocks of 100 and highlights the structure of its prime factorization.
| 100 | |||
| | | \ | ||
| 2 | 50 | ||
| | | \ | ||
| 2 | 25 | ||
| | | \ | ||
| 5 | 5 |
Factor Pairs of 100 (Visualization)
Factor pairs of 100 are sets of two numbers that, when multiplied together, result in 100. Factor pairs are symmetric and mirror around the square root of 100, such as (1, 100) and (100, 1), and can be both positive and negative pairs as long as their product equals 100.
| Negative factor pairs | Positive factor pairs |
|---|---|
| (-1, -100) | (1, 100) |
| (-2, -50) | (2, 50) |
| (-4, -25) | (4, 25) |
| (-5, -20) | (5, 20) |
| (-10, -10) | (10, 10) |
All factor pairs of 100 are (1, 100), (2, 50), (4, 25), (5, 20), (10, 10), (-1, -100), (-2, -50), (-4, -25), (-5, -20), (-10, -10).
Why Should I Care About Factors of 100?
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:
- Making Bracelets: You have 100 beads and want to make bracelets. If each bracelet requires 4 beads, you can make 25 bracelets because 4 × 25 = 100.
- Filling Bags: You have 100 candies to fill into treat bags. If each bag holds 10 candies, you will need 10 bags because 10 × 10 = 100.
- Planting Vegetables: You have 100 vegetable plants and want to plant them in equal rows. If each row has 10 plants, you’ll create 10 rows because 10 × 10 = 100.
- Arranging Chairs for a Concert: You have 100 chairs for a concert. If you arrange them into 4 rows, each row will have 25 chairs because 4 × 25 = 100.
- Filling Ice Trays: You have 100 ice cubes to freeze. If each tray holds 4 cubes, you’ll need 25 trays because 4 × 25 = 100.