Question

prime factorisation of 205000​

Answer 1

Prime factorization method of 205000 is given below.

$\begin{tabular}{c|l}2&205000\\ \cline{2-}2&102500\\ \cline{2-}2&51250\\ \cline{2-}5&25625\\ \cline{2-}5&5125\\ \cline{2-}5&1025\\ \cline{2-}5&205\\ \cline{2-}41&41\\ \cline{2-}&1\\ \cline{2-}\end{tabular}$

Thus 205000 can be written as,

$\huge 205000 = 2^3 \times 5^4 \times 41$

More information about 205000 from this:

  ⇒  205000 has three prime factors.

  ⇒  205000 has a total of 40 factors.

But there's no need to use the prime factorization method!

As the 205000 ends in 3 zeroes, we can say that 205000 is multiplied by 3 tens, hence there will be 3 twos and 3 fives in the prime factorization of 205000.

205000  =  205 × 1000  =  205 × 10³  =  205 × (2 × 5)³  =  205 × 2³ × 5³

The 205 thus obtained can be undergone prime factorization, thus,

205000  =  205 × 2³ × 5³  =  41 × 5 × 2³ × 5³  =  2³ × 5⁴ × 41

That's all!!!