What are all the factors, the prime factorization, and factor pairs of 4?

Factors are integral building blocks in mathematics that represent numbers we multiply together to yield a product. With 4 as our illustrative example, understanding factors reveals the underlying structure and mathematical properties inherent in the number 4. In essence, factors provide insights into how numbers interact and combine within the realm of mathematics.

Factors of 4 are the whole numbers that can be multiplied in pairs to produce the number 4. These factors effectively demonstrate the divisible characteristics of 4. Below is a visual representation alongside a list of factors for the number 4:

• 1 x 4 = 4
• 2 x 2 = 4

The factors of 4, therefore, are 1 and 2.

To determine the factors of 4 by division, we start by dividing 4 by integers less than or equal to itself. If the division yields a whole number, that divisor is considered a factor:

• 4 ÷ 1 = 4
• 4 ÷ 2 = 2
• 4 ÷ 4 = 1

Here, the divisors 1, 2, and 4 are the factors we sought. The division method provides a clear path to identifying the factors of any given number.

Pair factors of 4 are the two numbers, which when multiplied together result in the number 4. Here are positive and negative pair factors of 4:

• (1, 4)
• (2, 2)
• (-1, -4)
• (-2, -2)

These pairs illustrate the concept that both positive and negative numbers can serve as factors of 4, maintaining a balance in the number system.

The prime factorization of 4 requires breaking it down into its prime factors. These are the prime numbers that, when multiplied together, equal 4. Follow these steps for prime factorization:

• Start with the smallest prime number that divides 4, which is 2.
• Divide 4 by 2 to get 2.
• Since 2 is a prime number, it is another prime factor of 4.

The prime factorization of 4 can be represented as 2 x 2 or \(2^2\).

Understanding the factors of 4 provides several key insights:

• 4 has three positive factors: 1, 2, and 4.
• The prime factors of 4 are 2.
• Pair factors of 4 are (1, 4) and (2, 2), with their negative counterparts being (-1, -4) and (-2, -2).
• The sum of all factors of 4 is 7 (1+2+4).

These properties of 4 help us appreciate its simplicity and utility in various mathematical contexts.

• Write down all pair factors of 4.
• What is the prime factorization of 4?

The pair factors of 4 are (1, 4) and (2, 2). The prime factorization of 4 is \(2^2\) or 2 x 2.