Question

I hope this makes sense, but my teacher said he wants all exponents in the prime factorization, the example he gave was,
4^2
he wants 2^4
Is there a simple way to figure it out? for example, i'm trying to figure out 10^4.

Answer 1

Prime factorization just means breaking any number into prime numbers.

10^4= 10,000. The easiest method is to just divide this number my prime numbers until it can't be divided any further. It's a good idea to start dividing with the smallest primes, like 2.

10,000/2=5,000
5,000/2=2,500
2,500/2=1,250
1,250/2=625
-Alright once we divided by 2, the smallest prime, 4 times, we can no longer continue dividing by 2, so we move onto larger primes. 3 does not divide evenly into 625, but 5 does.
625/5=125
125/5=25
25/5=5
5/5=1
-Ok, we can stop now because no prime we try will divide evenly into 1.

So we divided by 4 four times, and divided by 5 four times. Basically:
2*2*2*2*5*5*5*5=10^4 (10,000)
do
2^4*5^4=10^4

So the prime factorization is: (2^4)*(5^4)