A positive integer n is divisible by 14, 15 and 175 but n is not divisible by 28, 45 or 1225. Furthermore, n divides 44100. Find the possible values of n.
prime factors
14: 2,7 but not 28: 2,2,7
15: 3,5 but not 45: 3,3,5
175: 5,5,7 but not 1225: 5,5,7,7
So n has prime factors which include [2,7,3,5,5] but no additional 2 or 3 or 7
2*7*3*5*5 = 1050
n's prime factors: [2, 3, 5, 5, 7]
44100's prime factors: [2, 2, 3, 3, 5, 5, 7, 7]
The extra factors are: [2,3,7] which are the prohibited extra factors, so 1050 is the only solution.
|
|
Posted by Larry
on 2025-01-16 09:47:07 |
Solution
