A teacher shares 130 pencils and 205 erasers equally among the largest possible number of children. After the sharing, 4 pencils and 7 erasers are left over.
How many children received the items?

Remove the leftovers first: 130 - 4 = 126 pencils and 205 - 7 = 198 erasers were actually shared out. The number of children is HCF(126, 198). Since $126=2\times 3^2\times$ 7 and $198=2\times 3^2\times$ 11, HCF = $2\times 3^2=18$, so each child got 7 pencils and 11 erasers. Answering 75 uses the difference 205 - 130 without removing the leftovers; 9 is a common factor but not the greatest; 36 does not divide 126.