Question

Find
the number of
which are
factors of 15^2015
not factors of
15^2014​

Answer 1

Answer:

2 × 6 = 12,

but also 3 × 4 = 12,

and of course 1 × 12 = 12.

So 1, 2, 3, 4, 6 and 12 are factors of 12.

And also -1,-2,-3,-4,-6 and -12, because you get a positive number when you multiply two negatives, such as (-2)×(-6) = 12

Answer: 1, 2, 3, 4, 6, 12, -1, -2, -3, -4, -6, -12

Answer 2

Answer:

4031

Step-by-step explanation:

15^2014 = 5^2014 x 3^2014  (Break the number in multiples of prime)

Number of factors of 15^2014 = (2014 + 1 ) x (2014 + 1) = 4060225

15^2015 = 5^2015 x 3^2015  (Break the number in multiples of prime)

Number of factors of 15^2015 = (2015 + 1 ) x (2015 + 1) = 4064256

All the factors of 15^2014 are factors of 15^2015.

So, the remaining are 4064256 - 4060225 = 4031

Try to understand it with small examples like. 12^2 & 12^3