Calculating the Result of an Expression

Oct 13, 2025 by miodeya.com 45 views

Introduction

In this article, we will delve into mathematical calculations and prime factorization. We will start by calculating the result of a given expression and then move on to finding the prime factors of two numbers. Finally, we will determine the Least Common Multiple (LCM) of these two numbers.

Calculating the Result of an Expression

4.1. Calculate the result of the expression: $$950 - 215 + 1800 + 8$$

To calculate the result of the expression, we need to follow the order of operations (PEMDAS):

Subtract 215 from 950: $950 - 215 = 735$
Add 1800 to 735: $735 + 1800 = 2535$
Add 8 to 2535: $2535 + 8 = 2543$

Therefore, the result of the expression is 2543.

Prime Factorization

5.1. Write the prime factors of 168 and 320

Prime factorization is the process of finding the prime factors of a number. To find the prime factors of 168 and 320, we need to divide each number by prime numbers starting from 2.

Prime Factors of 168

The prime factors of 168 are:

$168 = 2 \times 2 \times 2 \times 3 \times 7$

Therefore, the prime factors of 168 are 2, 2, 2, 3, 7.

Prime Factors of 320

The prime factors of 320 are:

$320 = 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 2$

Therefore, the prime factors of 320 are 2, 2, 2, 2, 2, 5, 2.

Least Common Multiple (LCM)

5.2. Determine the LCM (Least Common Multiple) of 168 and 320

The LCM of two numbers is the smallest number that is a multiple of both numbers. To find the LCM of 168 and 320, we need to find the product of the highest power of each prime factor that appears in either number.

LCM of 168 and 320

The prime factors of 168 are 2, 2, 2, 3, 7 and the prime factors of 320 are 2, 2, 2, 2, 2, 5, 2.

The highest power of 2 that appears in either number is 5 (in 320) and the highest power of 3 that appears in either number is 1 (in 168). The highest power of 5 that appears in either number is 1 (in 320) and the highest power of 7 that appears in either number is 1 (in 168).

Therefore, the LCM of 168 and 320 is:

$LCM(168, 320) = 2^5 \times 3^1 \times 5^1 \times 7^1$

$LCM(168, 320) = 6720$

Therefore, the LCM of 168 and 320 is 6720.

Conclusion

Introduction

In our previous article, we delved into mathematical calculations and prime factorization. We calculated the result of a given expression, found the prime factors of two numbers, and determined the LCM of these two numbers. In this article, we will answer some frequently asked questions related to mathematical calculations and prime factorization.

Q&A

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate any multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: What is prime factorization?

A: Prime factorization is the process of finding the prime factors of a number. It involves dividing the number by prime numbers starting from 2 until we can no longer divide it.

Q: How do I find the prime factors of a number?

A: To find the prime factors of a number, follow these steps:

Start by dividing the number by 2.
If the number is divisible by 2, continue dividing it by 2 until it is no longer divisible.
Then, move on to the next prime number (3) and repeat the process.
Continue this process until you can no longer divide the number by any prime number.

Q: What is the Least Common Multiple (LCM)?

A: The LCM of two numbers is the smallest number that is a multiple of both numbers. It is found by multiplying the highest power of each prime factor that appears in either number.

Q: How do I find the LCM of two numbers?

A: To find the LCM of two numbers, follow these steps:

Find the prime factors of each number.
Identify the highest power of each prime factor that appears in either number.
Multiply these prime factors together to find the LCM.

Q: What is the difference between the LCM and the Greatest Common Divisor (GCD)?

A: The LCM of two numbers is the smallest number that is a multiple of both numbers, while the GCD is the largest number that divides both numbers. The GCD and LCM are related by the formula:

$LCM(a, b) \times GCD(a, b) = a \times b$

Q: How do I find the GCD of two numbers?

A: To find the GCD of two numbers, follow these steps:

Find the prime factors of each number.
Identify the common prime factors between the two numbers.
Multiply these common prime factors together to find the GCD.

Conclusion

In this article, we answered some frequently asked questions related to mathematical calculations and prime factorization. We hope that this article has provided you with a better understanding of these concepts and how to apply them in real-world situations.