What is the highest power of 2 that divides 60?

Answer 1

0.0333

Answer 2

One way to solve this problem is to do a prime factor tree for the number 60. We start dividing 60 into its various factors and divide those factors into their factors until only prime factors remain. Because we are looking for powers of 2, let's begin with 2*30

60=60

Start here.

2*30=60

Here, we factor out a 2 from 60.

2*(2*15)=60

Here, we factor out a 2 from 30. We chose 2 because, again, we are looking for powers of 2 that divide into 60.

2*2*(3*5)=60

Here, we factor a 3 out of 15. We chose 3 because 15 is not divisible by 2.

We now know that our prime factors of 60 are 2, 3, and 5. 2 appears twice, so we know that the largest power of 2 that divides into 60 is 22, or 4.

Look at the third line of the problem, "2*(2*15)=60." We see that 15 is not divisible by 2. Because we are looking only for powers of two, we could have stopped here. We know that no matter how many times we were able to factor 15, we would never get another 2.

There is another way to solve this problem, but it is clumsy. I call it a "scorched Earth" approach since it involves trying every possibility until a solution is found. These methods are unfavorable because more complex problems require vast amounts of time to solve and some problems simply cannot be solved this way.

Start by listing powers of 2 that are less than 60. We will stop then because we know that 60 is not divisible by any number larger than itself.

2,4,8,16,32

Then list all factors of 60

2,3,4,5,6,10,12,15,20,30

Then we find the largest number they have in common

4

We could also try dividing 60 by each of our powers of 2 to see which one is the largest we can divide evenly into 60. This also gives us an answer of 4.

While any of these methods work, the first is the easiest and most reliable and will work for any pair of numbers. The downside is that it requires a better understanding of math.