A mystery number is greater than 50 and less than 100. You can make exactly five different rectangles with the mystery number of tiles. Its prime factorization consists of only one prime number. What is the number???????????

Question

anonymous · Answer

Please help anyone please! Thank you!  🙂

anonymous · Answer

I would be so thankful if anyone would help me please!

victoriasushchik · Answer

this is exactly one of my assigments

victoriasushchik · Answer

a) the number is between 50 and 100 
b) it is an even number, can can be represented as the product of 5 even numbers (5 rectangles) 
c) it's prime factorization contains only 1 prime number 

By looking at b and c together, we can deduce that 5 is the prime number in the mystery number's factorization, so we know our number is a product of 5 and one or more non-primes. Since the non-primes must be even numbers, and we know the factors can only contain ONE prime, the remaining factors MUST be multiples of 2, so our number is 5*2^x such that 5*2^x > 50 and 5*2^x < 100: 

5*2*2*2*2 = 80 

Our mystery number is 80! 

I hope this helps!

anonymous · Answer

Thanks so much for your help!!!😊😊😊😊

victoriasushchik · Answer

your welcome hon!

retireed · Answer

I was always taught that 2 is a prime number.  So the question should have said something like only two prime numbers.  In my opinion.