What is the GCF of 16 and 128?

Nov 9, 2016

16

Explanation:

So this may seem like a long winded way of working it out, but it's good to get into a habit of using a method that will work for all issues.

The first thing you want to do is express both 16 and 128 as a product of their prime factors.

This means, we find what prime numbers are multiplied together to make them.
You can do this using a prime factor tree, where you just keep splitting the number into factors until they are prime and cannot be split any further.

You then organise the prime factors into a venn diagram, with shared factors in the middle.

To find the Greatest Common Factor, you multiply the factors in the middle. As there are four 2s in both circles, we just do 2 x 2 x 2 x 2, or ${2}^{4}$ (which is 16 itself!). This makes sense, as 16 can be multiplied by 8 to make 128, and is also the highest factor of 16 (1 x 16).

Again, I know this seems long winded, but for more complex problems, it's really useful to know!

I hope this helps; let me know if I can do anything else:)