kruttikaaggarwal wrote:
Hwo do we get to 16,000= (2^7)(5^3) Is it trial and error?
Final goal is to reach 1.When asking for prime factors we start with the smallest prime factor 2.
We can clearly see that in 16000 we would have many multiples of 2. So one way is to keep dividing by 2 till we can divide no more.
16000/2 = 8000 ...... one factor of 2
8000/2 = 4000 ..........second factor 2
.
.
1000/2= 500 .............. 5th factor factor of 2
.
250/2=125 ................. 7th Factor of 2
Now we need other prime factors so we move on to higher prime number such as 3 and 5.
Division by 3 is not possible so 5
125 can be divided 3 times with 5 to get 1.
Hence \(16000=2^7 \times 5^3\)
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