Count up in fours
Start at 0 and count up in fours: 4, 8, 12, 16, 20, 24, 28, and on. The numbers you land on are called the multiples of 4.
Each multiple of 4 is 4 times a whole number. 4 is 1 × 4, 8 is 2 × 4, 12 is 3 × 4, and 28 is 7 × 4. So a multiple of 4 is also a number that 4 divides exactly: 28 ÷ 4 = 7.
2 jumps of 4 = 8
Count on to 40 in jumps of 4
Move the count on in jumps of 4. Every number it lands on is ringed, and the ringed numbers are the multiples of 4.
A whole number of jumps
On a number line, a multiple of 4 is a whole number of jumps of 4 away from 0. 12 is 3 jumps, because 3 × 4 = 12.
14 is not a multiple of 4. Three jumps reach 12, and a fourth jump goes past 14 to 16. 14 ÷ 4 = 3 remainder 2, and that remainder is why no jump lands on 14.
Three jumps of 4 from 0 land on 4, 8 and 12.
They never stop
However far you count, one more jump of 4 always makes another multiple. 400 is a multiple of 4, because 100 × 4 = 400, and so is 404. So the list of multiples of 4 never ends.
Two slips
A number next to a multiple is not a multiple. 29 is one more than 28, and 29 ÷ 4 leaves 1, so counting in fours steps over it. 27 is one less, and 27 ÷ 4 leaves 3.
The number itself is on its own list. The first multiple of 4 is 1 × 4 = 4, so 4 is a multiple of 4.