four integers that are mutually relatively prime?

Question

can you find four integers that are mutually relatively prime (i.e., their greatest common divisor is 1), but any three of those integers are not mutually relatively prime?

Answer 1

Hi,
30, 42. 70, and 105 are mutually relatively prime.

Their factors are listed:

30 -2,3,5
42 -2,3,7
70 -2,5,7
105 -3,5,7

30, 42, and 70 have a GCF of 2 that 105 does not have.
30,42, and 105 have a GCF of 3 that 70 does not have.
30,70, and 105 have a GCF of 5 that 42 does not have.
42,70, and 105 have a GCF of 7 that 30 does not have.


I hope that helps!! :-)

Answer 2

I think you're asking for ANY three to be not mutually prime.

So you need prime numbers spread among the four, as follows:
abc = 2*3*5 = 30
bcd = 3*5*1 = 15
acd = 2*5*1 = 10
abd = 2*3*1 = 6

You can use any four prime numbers (including one) in that manner.

So, that's the simplest solution. However, those are not integers.

Answer 3

2,3,5,7,11