The factors of a number are the integers that divide that number without leaving a remainder. To find the factors of 32,256, we can start with the prime factorization of the number.
First, let’s perform the prime factorization:
- 32,256 can be expressed as: 32,256 = 2^{8} imes 3^{2}
This means that 32,256 is the product of the prime number 2 raised to the 8th power and the prime number 3 raised to the 2nd power.
Now we can calculate the factors by taking all combinations of these prime factors.
The complete set of factors of 32,256 can be generated by combining these prime factors in different ways:
- 1
- 2
- 4
- 8
- 16
- 32
- 3
- 6
- 12
- 24
- 48
- 96
- 9
- 18
- 36
- 72
- 144
- 288
- 256
- 512
- 768
- 1024
- 2048
- 3024
- 6144
- 8192
- 16384
- 32,256
It’s also interesting to note that factors can be paired together. For example, if we take 2 as a factor, we can pair it with 16,128 because:
- 2 x 16,128 = 32,256
Understanding factors is important in various mathematical applications, including simplifying fractions, finding common denominators, and solving equations. So, the factors of 32,256 give insight into the number’s composition and its characteristics.