The number 1369 could be factored like: 1*1369 or 37*37.

Therefore the possible nummers are 1, 1369 and 37 each of which divides 1369 cents equally without remainder. Or

1369=1*1369 or 139=37*37. So,

1369/1 = 1369 and  1369/1369=1  or

1369/37 = 37.

So, having only one man group is a possible answer, but one man group looks little strange.

Having 1369 members is also possible and the bill could be shared equally each getting one cent. But the group is very large.

So the ideal number of men in the group is 37 , which may also be large,without any other better alternative, and each man gets 1369/37=37 cents as his equal share of th