The largest number which divides 60 and 75 leaving remainders 8 and 10 respectively is

52 and 65

Step-by-step explanation:

dividend - divisor*quotient = remainder

We want to find the largest number which divides 60 leaving remainders 8. The largest divisor is obtained when the quotient is 1. Replacing into the previous equation:

60 - divisor*1 = 8

60 - 8 = divisor

52 = divisor

In the second case, the dividend is 75, the quotient is 1 again, and the remainder is 10, then:

75 - divisor*1 = 10

75 - 10 = divisor

65 = divisor