Factoring formula doesn't seem to always work?

[gxj007]

How many factors in a given number?

Step 1: Express the number as a product of powers of prime numbers.

In this case, 48 can be written as 16 * 3 = (2^4 * 3)

Now, add 1 to the power of each of the prime number and multiply the result.

So I would get: (4 + 1)*(1 + 1) = 5 * 2 = 10 factors (the power of 2 is 4 and the power of 3 is 1)

But this rule doesn’t seem to work for 64 ?

Prime numbers are 2^6. So 6+1 = 7 but the number of total factors is 8? So is it safe to say that in a case when there is only 1 prime number, you need to just add 1 to your total. In this case I would then have 6+1+1 = 8, which is now correct?

thanks

[parallel_chase]

How many factors in a given number?

Step 1: Express the number as a product of powers of prime numbers.

In this case, 48 can be written as 16 * 3 = (2^4 * 3)

Now, add 1 to the power of each of the prime number and multiply the result.

So I would get: (4 + 1)*(1 + 1) = 5 * 2 = 10 factors (the power of 2 is 4 and the power of 3 is 1)

But this rule doesn’t seem to work for 64 ?

Prime numbers are 2^6. So 6+1 = 7 but the number of total factors is 8? So is it safe to say that in a case when there is only 1 prime number, you need to just add 1 to your total. In this case I would then have 6+1+1 = 8, which is now correct?

thanks

it always work

lets find the factors of 2^6

1, 2, 2^2, 2^3, 2^4, 2^5, 2^6 = 7 factors

how are you getting 8 ?

[gxj007]

thanks. I was factoring 64 out in pairs and was counting 8*8 twice. Yes, there are 7 factors...my bad.