The number 400 is a positive integer that has several factors. In mathematics, a factor of a number is an integer that can be multiplied by another integer to produce the original number. To find the factors of 400, we need to identify all the numbers that divide 400 without leaving a remainder.
Prime Factorization of 400
The prime factorization of 400 is 2^4 * 5^2. This means that the number 400 can be expressed as the product of its prime factors, which are 2 and 5. The exponent 4 indicates that the prime factor 2 is raised to the power of 4, and the exponent 2 indicates that the prime factor 5 is raised to the power of 2.
Calculating Factors of 400
Using the prime factorization of 400, we can calculate all the factors of 400. To do this, we need to find all the possible combinations of the prime factors 2 and 5. The factors of 400 are: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, and 400.
| Factor | Prime Factorization |
|---|---|
| 1 | 1 |
| 2 | 2^1 |
| 4 | 2^2 |
| 5 | 5^1 |
| 8 | 2^3 |
| 10 | 2^1 * 5^1 |
| 16 | 2^4 |
| 20 | 2^2 * 5^1 |
| 25 | 5^2 |
| 40 | 2^3 * 5^1 |
| 50 | 2^1 * 5^2 |
| 80 | 2^4 * 5^1 |
| 100 | 2^2 * 5^2 |
| 200 | 2^3 * 5^2 |
| 400 | 2^4 * 5^2 |
Real-World Applications of Factors of 400
The factors of 400 have several real-world applications. For example, in geometry, the factors of 400 can be used to find the area of a rectangle with a length of 20 units and a width of 20 units. The area of the rectangle is 400 square units, which can be factored into 20 * 20.
Factors of 400 in Finance
In finance, the factors of 400 can be used to calculate interest rates and investments. For example, if an investor invests 400 at an annual interest rate of 5%, the interest earned after one year is 20, which is a factor of 400.
In conclusion, the factors of 400 are an essential concept in mathematics, with several real-world applications in geometry, finance, and other fields. Understanding the factors of 400 can help individuals solve problems and make informed decisions in their personal and professional lives.
What are the factors of 400?
+The factors of 400 are: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, and 400.
How do you calculate the factors of 400?
+To calculate the factors of 400, you need to find all the possible combinations of the prime factors 2 and 5. The prime factorization of 400 is 2^4 * 5^2.
What are some real-world applications of the factors of 400?
+The factors of 400 have several real-world applications in geometry, finance, and other fields. For example, in geometry, the factors of 400 can be used to find the area of a rectangle, and in finance, the factors of 400 can be used to calculate interest rates and investments.
