What are Johan's lock numbers?

Question

Johan remembers that 2 of the 3 different numbers he uses to open his combination lock are divisible by 4, and the third number is divisible by 7. The sum of all 3 numbers is 44. But he can't remember the numbers or their order. The lock uses only even integers, and the largest number is 40. What are Johan's lock numbers?

Answer 1

the largest is 40

all are even

one is divisible by 7

even and divisible by 7 gives you only 2 possibilities, 14 and 28

the sum is 44

44-28=16

16=12+4

4 and 12 are divisible by 4

28 is divisible by 7

4, 12, and 28 are all even

4+12+28=44

4, 12, and 28 are the numbers (the other possibility, 14, doesn't work: 44-14=30 and 30 can't be expressed as the sum of 2 multiples of 4 because 30 is not a multiple of 4; if you add 2 multiples of 4 you must get another multiple of 4) (notice that 16 is a multiple of 4)