If 79 is a prime number, then identify the prime factors of 44 ; if it is not a prime number then identify the prime factors of 18. A. 2 B. 3 C. 5 D. 7 E. 11

Prime factorization is a method of expressing a composite number as a product of its prime numbers. Prime numbers are numbers that are only divisible by 1 and themselves. An example will help to illustrate this.
Let's take the number 44. To find its prime factors, we start by dividing it by the smallest prime number, which is 2. Since 44 is even, it's divisible by 2:

• 44 ÷ 2 = 22

22 is also even, so divide it by 2 again:

• 22 ÷ 2 = 11

The number 11 is a prime number because it is only divisible by 1 and itself. So, the prime factorization of 44 is:

• 2 × 2 × 11

Understanding prime factorization helps in simplifying fractions, finding the greatest common divisors, and working through various mathematical problems, including GMAT problem-solving exercises.

Prime numbers are numbers that have exactly two distinct positive divisors: 1 and the number itself. This means that they cannot be divided evenly by any other numbers. Examples of prime numbers include 2, 3, 5, 7, 11, 13, and so on. Notice that 2 is the only even prime number.
To determine if a number is prime, check if it is not divisible evenly by any prime number less than or equal to its square root. Consider the number 79 from the exercise. Check its divisibility by prime numbers less than or equal to \(\sqrt{79}\).

• \(\sqrt{79}\)\ is approximately 8.9, so we check divisibility by 2, 3, 5, and 7.

Since 79 is not divisible by any of these, it is confirmed to be a prime number. Identifying prime numbers quickly is essential in prime factorization and in solving many standardized test problems.

Basic arithmetic operations include addition, subtraction, multiplication, and division. These operations are fundamental to all areas of mathematics. Here’s a refresher on each:

Addition (+): Combining two numbers to get their total. For instance, 2 + 3 = 5.

• Examples: 4 + 7 = 11, 10 + 15 = 25

Subtraction (-): Taking one number away from another. For instance, 5 - 2 = 3.

• Examples: 13 - 5 = 8, 20 - 9 = 11

Multiplication (×): Repeated addition of a number. For instance, 4 × 2 = 8 means adding 4 twice.

• Examples: 6 × 3 = 18, 7 × 4 = 28

Division (÷): Splitting a number into equal parts. For example, 8 ÷ 2 = 4.

• Examples: 16 ÷ 4 = 4, 21 ÷ 3 = 7

In solving the exercise, understanding division is crucial for prime factorization. By dividing 44 by 2, we simplified the factorization process. Regular practice in these operations builds a strong foundation for tackling more complex problems.