Without using a calculator, decide which of these numbers divide into 2^5 * 3^9 * 7^2 * 13^5 8 17^4 * 19 with no remainder. Explain how you know.

Question

a) 2^4 * 3^8 * 7^2 * 13^4 * 17^4 *

b) 2^5 * 3^2 * 5 * 7^2* 17

c) 2^4 * 13^4 * 17^4 * 19^4

d) 2^2 * 3^5 * 7 * 13^3 * 17^2 * 19

Answer 1

all divisors must have the same list of primes, with powers the same or less.

(b) does not work, since the dividend does not include a 5.

so, what is your answer?

Answer 2

I don't really understand that, doesn't b have a five in there?

Answer 3

yes, but b is the divisor

For it to divide the big number above (the dividend), there must also be a 5 there.

Answer 4

Ohhhh! Thank you!

Answer 5

I still dont get it. Can you explain the answer a bit more detailed?