How do you find all the factors of 54?

Answer 1

First, we notice it is even. Write 2 as a prime factor and divide it out.
Now we have 27, which we notice is divisible by 3.
We divide by 3 until we can't, and notice we do it three times and end up at 1.
When we have 1, then we know all the prime factors.
In this case, we have 54 = 2*3*3*3 = 2*33.= 21*33
Notice the exponents are 1 and 3
So we add one to these and multiply: 2*4 = 8.
This means 54 has 8 factors, so we'll know if we miss any.
To find the factors, just look for all the ways we can multiply with one 2 and three 3s.
We have, 1, 2, 3, 6, 9, 18, 27, and 54.
As there are eight, we know we didn't miss any.