108的因数是指能够整除108的所有正整数,我们可以通过分解质因数的方法找到108的所有因数。
将108分解为质因数:$108 = 2 \times 2 \times 3 \times 3 \times 3$,这是一个五次方数。
我们可以通过计算所有可能的质因数组合来找到108的所有因数,对于每个质因数,我们可以选择使用它0次、1次、2次等,直到它的最大次数(在这个例子中是5次),我们有以下组合:
- $2^0 \times 3^0 = 1$
- $2^1 \times 3^0 = 2$
- $2^2 \times 3^0 = 4$
- $2^3 \times 3^0 = 8$
- $2^0 \times 3^1 = 3$
- $2^1 \times 3^1 = 6$
- $2^2 \times 3^1 = 12$
- $2^3 times 3^1 = 24$
- $2^0 \times 3^2 = 9$
- $2^1 \times 3^2 = 18$
- $2^2 \times 3^2 = 36$
- $2^3 \times 3^2 = 72$
- $2^0 \times 3^3 = 27$
- $2^1 \times 3^3 = 54$
- $2^2 \times 3^3 = 162$
- $2^3 times 3^3 = 486$
- $2^0 \times 3^4 = 81$
- $2^1 \times 3^4 = 162$
- $2^2 \times 3^4 = 546$
- $2^3 \times 3^4 = 2166$
- $2^0 \times 3^5 = 243$
- $2^1 \times 3^5 = 729$
- $2^2 \times 3^5 = 3024$
- $2^3 \times 3^5 = 18144$
- $2^0 \times 3^6 = 729$
- $2^1 \times 3^6 = 5488$
- $2^2 \times 3^6 = 16796$
- $2^3 \times 3^6 = 49896$
- $2^4 \times 3^6 = 798916/7=79891.../7 (整除)