List the factors of 24.
The Correct Answer and Explanation is:
To find the factors of 24, we need to identify all the integers that can divide 24 evenly without leaving a remainder. A factor is a number that can be multiplied by another number to yield the original number. The factors of 24 are:
1, 2, 3, 4, 6, 8, 12, and 24.
Detailed Explanation of Factors of 24
Definition of Factors:
Factors of a number are those integers which can divide that number evenly, meaning the result is a whole number without any remainder. For example, if we divide 24 by 6, we get 4, which is a whole number, indicating that 6 is a factor of 24.
Finding Factors:
To find the factors of 24, we can start by dividing 24 by the smallest integers, beginning with 1, and moving upward. We proceed as follows:
- 1: 24 ÷ 1 = 24
- 2: 24 ÷ 2 = 12
- 3: 24 ÷ 3 = 8
- 4: 24 ÷ 4 = 6
- 6: 24 ÷ 6 = 4
- 8: 24 ÷ 8 = 3
- 12: 24 ÷ 12 = 2
- 24: 24 ÷ 24 = 1
As we see, dividing by these numbers results in whole numbers.
Characteristics of Factors:
Factors come in pairs. For instance, if 2 is a factor, then 12 is also a factor since 2 × 12 = 24. Notably, factors of a number are always less than or equal to that number.
Prime Factorization:
Another approach to finding factors is through prime factorization. The prime factorization of 24 is:
[ 24 = 2^3 \times 3^1 ]
From the prime factorization, we can derive all combinations of these prime factors to list all the factors. Each combination yields one of the factors listed above.
In conclusion, the complete set of factors of 24—1, 2, 3, 4, 6, 8, 12, and 24—demonstrates the integer’s versatility in division and multiplication within mathematics.