Factors are numbers that divide another number completely without leaving a remainder. In this article, we will explore the factors of 2024, breaking it down into simple steps. We will also introduce a free tool to help you find factors of any number easily.
What Are Factors?
Factors of a number are integers that divide the number exactly. For example, factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers divides 12 without leaving a remainder.
Finding Factors of 2024
To find the factors of 2024, follow these steps:
- Determine the Prime Factors of 2024:
Prime factors are the basic building blocks of a number. Start by dividing 2024 by the smallest prime number (2) and continue dividing by prime numbers until you can’t divide anymore. - List the Prime Factors:
Write down the prime factors you found. These will help you determine all the factors of 2024. - Generate All Factors:
Use the prime factors to list all combinations that multiply to give 2024.
Step-by-Step Solution:
- Find Prime Factors:
- Divide 2024 by 2:
( 2024 ÷ 2 = 1012 ) - Divide 1012 by 2:
( 1012 ÷ 2 = 506 ) - Divide 506 by 2:
( 506 ÷ 2 = 253 ) - 253 is not divisible by 2, so try the next prime number, which is 3. Since 253 ÷ 3 is not an integer, try 5 next. It doesn’t work either.
- Try 7:
( 253 ÷ 7 = 36.14 ) (not an integer) - Try 11:
( 253 ÷ 11 = 23 ) (which is a prime number) So, the prime factorization of 2024 is:
( 2024 = 2^3 × 11 × 23 )
- List the Prime Factors:
- ( 2^3 = 8 )
- Prime factors are: 2, 11, 23
Generate All Factors:
The actual factors of 2024 are:
| Factor | Calculation |
|---|---|
| 1 | 2024÷1=2024 |
| 2 | 2024÷2=1012 |
| 4 | 2024÷4=506 |
| 8 | 2024÷8=253 |
| 32 | 2024÷32=63 |
| 63 | 2024÷63=32 |
| 1012 | 2024÷1012=2 |
| 2024 | 2024÷2024=1 |
Factor Pairs of 2400:
(1, 2400)
(2, 1200)
(3, 800)
(4, 600)
(5, 480)
(6, 400)
(8, 300)
(10, 240)
(12, 200)
(15, 160)
(16, 150)
(20, 120)
(24, 100)
(25, 96)
(30, 80)
(32, 75)
(40, 60)
(48, 50)
(50, 48)
(60, 40)
(75, 32)
(80, 30)
(96, 25)
(100, 24)
(120, 20)
(150, 16)
(160, 15)
(200, 12)
(240, 10)
(300, 8)
(400, 6)
(480, 5)
(600, 4)
(800, 3)
(1200, 2)
(2400, 1)
Summary
The factors of 2024 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, and 2400.
For more help with finding factors of any number, check out our free tool: Factor Calculators. This tool will quickly provide the factors of any number you input, making calculations easier and faster.
Feel free to reach out if you have any questions or need further assistance!