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.
14 = 2 * 7
15 = 3 * 5
175 = 5 * 5 * 7
2 * 3 * 5 * 5 * 7 = 1050 covers all of these.
44100 = 1050 * 42 = 1050 * 2 * 3 * 7
Any combination of 2, 3, 7 (including all or none) can be used to multiply 1050, but no more than one of each. The possible numbers are:
1050, 2100, 3150, 7350, 6300, 14700, 22050, 44100
However, the requirement that n is not divisible by 28, 45 or 1225 actually precludes all the extra values.
Only n = 1050 remains.
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Posted by Charlie
on 2025-01-16 09:51:39 |
solution
