What is the greatest common factor of 43 and 128?

Answer 1

The greatest common factor for 43 and 32 is 1.

Method 1:

Factoring completely, we determine that:

32 = 2 * 2 * 2 * 2 * 2 * 1

43 = 43 * 1

The only factor that these two have in common is 1, making this the greatest common factor.

Method 2:

We notice that 32 is a power of 2 (2 ^ 5, to be exact), so its only unique factors are 1 and 2. Since 43 is odd, it does not have 2 as a factor. Therefore, the only factor that they could have in common is 1, making that the greatest common factor.

Method 3:

We notice that 43 is a Prime number, meaning that its only factors are 1 and itself. Since 32 is not a multiple of 43 (impossible, being smaller), the only common factor they could have is 1.

Answer 2

It is: 1

Answer 3

The GCF is 64.