Answer:
To determine if the expression 100000x+100y+10z or 100000x+100y+z is divisible by 3, 7, 13, and 37, you can use the divisibility rules for each number.
Divisibility by 3: To check if a number is divisible by 3, you can add up the digits of the number, then check if the sum is divisible by 3.
Divisibility by 7: To check if a number is divisible by 7, you can subtract twice the last digit from the remaining number, then check if the result is divisible by 7.
Divisibility by 13: To check if a number is divisible by 13, you can subtract 10 times the last digit from the remaining number, then check if the result is divisible by 13.
Divisibility by 37: To check if a number is divisible by 37, you can subtract 30 times the last digit from the remaining number, then check if the result is divisible by 37.
By applying these divisibility rules to the expression 100000x+100y+10z or 100000x+100y+z, you can determine if it is divisible by 3, 7, 13, and 37.