Nothing left over
Arrange 12 squares in rows of 3. The squares make 4 full rows, and no square is left over.
When a division leaves nothing over, we say that one number divides the other exactly. Here 3 divides 12 exactly: 12 ÷ 3 = 4, and the remainder is 0. Multiplying back gives every square: 4 × 3 = 12.
12 squares make 4 full rows of 3, with none left over.
Something left over
Now arrange 11 squares in rows of 5. Two rows fill up, using 2 × 5 = 10 squares, and 1 square is left over. One square cannot make another row of 5.
So 11 ÷ 5 = 2 remainder 1. The remainder is not 0, so 5 does not divide 11 exactly.
11 in groups of 5: two full groups, and 1 left over.
Exactly means a remainder of 0
To find out whether one number divides another exactly, divide and look at the remainder. A remainder of 0 means it divides exactly. Any other remainder means it does not.
Start with 10 counters in groups of 3. Three groups fill, and 1 counter is left over, so 3 does not divide 10 exactly. Add one counter and there are 2 left over, so 3 does not divide 11 either. Add one more, and the last group fills: 3 divides 12 exactly.
10 = 3 × 3 + 1: 3 full bags and 1 left over, fewer than 3, so another bag still needs 2: 1 + 2 = 3
Add items one at a time until the remainder resets
Each bag holds 3. Add counters one at a time until the last bag is full and the remainder is 0.
Which number divides which
Say the numbers in the right order. 3 divides 12, because 12 shares into groups of 3 with nothing left over. 12 does not divide 3: 3 is smaller than 12, so it cannot make even one group of 12.