What are all the factors, the prime factorization, and factor pairs of 24?

Factors are the fundamental building blocks in mathematics that we use to break down numbers. Focusing on the number 24 as an illustrative example, factors are the integers that we can multiply together to achieve the product of 24. A deeper understanding of factors reveals the unique composition and attributes of 24, unlocking insights into its mathematical relationships and applications.

The concept of factors for the number 24 relates to finding all the integers that can multiply in pairs to produce 24. A definitive list of factors for 24 can be visually represented, ensuring we comprehend the multiplication pairings fully, as shown in the table below:

• 1 × 24 = 24
• 2 × 12 = 24
• 3 × 8 = 24
• 4 × 6 = 24

To determine the factors of 24, we employ the division method. Any whole number less than or equal to 24 can be tested as a potential factor through division. If the number divides 24 with a whole number quotient, it is indeed a factor. Here’s a step-by-step breakdown of this approach:

• 24 ÷ 1 = 24, hence 1 and 24 are factors.
• 24 ÷ 2 = 12, indicating 2 is a factor, and so on.

This method is repeated with other whole numbers. However, if the quotient is not a whole number, it is not a factor, as shown:

• 24 ÷ 5 = 4.8, not a whole number, hence 5 is not a factor.

Thus, we determine that the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

Pair factors of 24 are groups of two numbers that give 24 when multiplied together. Both positive and negative number pairs qualify as pair factors, provided their multiplication equates to 24. Below is a comprehensive list of pair factors for the number 24:

The prime factorization of 24 involves breaking it down into its prime number constituents, which are the set of numbers that multiply to yield 24, and are also prime. A factor tree is a useful visual tool to display this. Below is the result of the prime factorization of 24:

• 24 = 2 × 2 × 2 × 3
• 24 = 2³ × 3

This indicates that the prime factors of 24 are 2 and 3.

Key Points on Factors of 24

• Total factors of 24: 8 (1, 2, 3, 4, 6, 8, 12, 24)
• Prime factors of 24: 2, 3
• Pair factors of 24: Both positive and negative pairs that multiply to 24
• Sum of all factors of 24: 60

Through the exploration of these factors, we discover that 24 has a rich and varied factor structure that can be applied in many mathematical problems and real-world situations.