Explanation:
counting numbers means whole numbers.
these divisible rules mean numbers that are divisible by 4 and by 3 and by 5.
4 = 2×2
so, everything that is divisible by 4 is also divisible by 2.
6 = 2×3
everything that is divisible by 2 and by 3 is also divisible by 6. therefore everything that is divisible by 4 and by 3 is also divisible by 6.
5 is a prime number on its own.
so, we are looking for all numbers that are divisible by
3×4×5 = 60
the smallest common multiple of 2, 3, 4, 5 and 6.
formally we get this by the combination of the longest chains of the prime factors :
2 = 2
3 = 3
4 = 2×2
5 = 5
6 = 2×3
the longest chain of 2 is 2×2.
the longest chain of 3 is 3.
the longest chain of 5 is 5.
so, 2×2×3×5 = 60
therefore, our solution is all numbers divisible by 60.
that means all multiples of 60 between 200 and 500.
what is the lowest number for that ?
3×60 = 180 too low
4×60 = 240 ok
what is the highest number ?
8×60 = 480 ok
9×60 = 540 too high
so, we only have
4×60 = 240
5×60 = 300
6×60 = 360
7×60 = 420
8×60 = 480
we have 5 numbers between 200 and 500 that are divisible by all of 2, 3, 4, 5 and 6.