What Factors of 48 Add Up to -14?

The prime factorization of 48 is 2⁴ * 3. So, the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

The only two factors of 48 that add up to -14 are -24 and -8. This is because -24 + -8 = -32, and 48 – 32 = 16.

How to Find Factors of a Number

To find the factors of a number, you can use the following steps:

1. Find all the prime numbers that divide the number.
2. For each prime number, find all the powers of that prime number that divide the number.
3. Multiply the prime numbers and their powers together to get all the factors of the number.

Why Factors of a Number Matter

Factors of a number are important for a variety of reasons. For example, they can be used to:

• Find the greatest common factor (GCF) of two numbers
• Find the least common multiple (LCM) of two numbers
• Solve equations involving fractions
• Simplify algebraic expressions
• Find the area and volume of geometric shapes

Applications of Factors of Numbers

Factors of numbers have a wide range of applications in mathematics and other fields. Here are a few examples:

• In geometry, factors of numbers are used to find the area and volume of geometric shapes. For example, the area of a rectangle is equal to the product of its length and width, and the volume of a cube is equal to the cube of its side length.
• In algebra, factors of numbers are used to simplify algebraic expressions. For example, the expression (x + 2)(x – 3) can be simplified to x² – x – 6 by factoring out the common factor of (x + 2).
• In number theory, factors of numbers are used to study the properties of numbers. For example, the prime factorization of a number can be used to determine whether the number is prime or composite.

Conclusion

Factors of numbers are a fundamental concept in mathematics with a wide range of applications. By understanding how to find and use factors of numbers, you can solve a variety of problems and gain a deeper understanding of mathematics.

Here are some additional examples of how factors of numbers can be used:

• In computer science, factors of numbers are used to design efficient algorithms for a variety of tasks, such as finding the greatest common divisor of two numbers or finding the prime factorization of a number.
• In cryptography, factors of numbers are used to create encryption algorithms that are difficult to break.
• In finance, factors of numbers are used to calculate interest rates and other financial calculations.

As you can see, factors of numbers are a versatile and important concept with a wide range of applications in a variety of fields.