Question

Find the greatest common factor. $$20,32,40$$

Short answer

The greatest common factor of 20, 32 and 40 is \(2^2\) = 4.

Step-by-step solution

Prime Factorization for Each Number

First, find the prime factorization for each of the numbers. Here's how you do it: \nFor 20, the prime factorization is \(2^2*5\);\nFor 32, the prime factorization is \(2^5\); \nFor 40, the prime factorization is \(2^3*5\).

Find the Common Prime Factors

Now, check which prime factors are common in all the numbers: \nFrom the prime factorizations of 20, 32, and 40, we can see they all have the prime factors 2.

Lowest Power of common Prime Factors

Check the lowest power of the common prime factor(s). \nFor the number 2, the lowest power is \(2^2\) which comes from 20. This is because you can only 'not leave a remainder' if you extract from each number '1' times the same, neatly dividable packet. Extracting 5 from each number would not be possible, thus \(2^2\) is the best we can do.