In mathematics, a factor is an integer that divides another integer without leaving a remainder. Factors are important in various mathematical operations, such as simplifying expressions, finding the greatest common divisor (GCD), and solving problems efficiently. The process of finding all the factors of a number is called factorization. This can be done by dividing the number by integers from 1 to the number itself and checking if the division results in an integer. A number can also be expressed through its prime factorization, which is the product of its prime factors.
A factor of a number is an integer that divides the number without leaving a remainder. Essentially, a factor is a number that, when multiplied by another number, gives the original number. The factors of 96 are the integers that can be multiplied together to result in 96. The factors of 96 are:
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
These factors can be written in pairs as well, which helps in understanding their relationship better.
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To calculate the factors of 96, follow these steps:
Here's a table showing the division process:
| Divisor | Result | Is a Factor? |
|---|---|---|
| 1 | 96 | Yes |
| 2 | 48 | Yes |
| 3 | 32 | Yes |
| 4 | 24 | Yes |
| 5 | 19.2 | No |
| 6 | 16 | Yes |
| 8 | 12 | Yes |
| 9 | 10.67 | No |
| 12 | 8 | Yes |
| 16 | 6 | Yes |
| 24 | 4 | Yes |
| 32 | 3 | Yes |
| 48 | 2 | Yes |
| 96 | 1 | Yes |
These calculations confirm that the factors of 96 are indeed 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
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The prime factorization of a number is expressing the number as the product of its prime factors. For 96, this can be done by continuously dividing the number by its smallest prime factor:
So, the prime factorization of 96 is 25×3
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To find the pairs of factors of 96, list all combinations of the factors that multiply to give 96:
These pairs show how the factors relate to each other.
The prime factorization of 96 is 2 x 2 x 2 x 2 x 2 x 3, which can be expressed as 2⁵ x 3.
The first 10 multiples of 96 are 96, 192, 288, 384, 480, 576, 672, 768, 864, and 960. The sum of these multiples is 5280.
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
No, 96 is not a perfect square.
No, 96 is not a factor of 24, but 24 is a factor of 96.
Yes, 8 is a factor of 96. The factors of 96 include 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.