Divisible means capable of being divided evenly by another number, with nothing left over. When 12 is divisible by 3, you can split 12 items into groups of 3 with no remainder: 12 ÷ 3 = 4 exactly.

Think about sharing 20 cookies among 5 friends. Since 20 is divisible by 5, each person gets exactly 4 cookies and there are none left over. But if you tried splitting 20 cookies among 7 friends, it wouldn't work out evenly because 20 isn't divisible by 7. Someone would get an extra piece, or you'd have leftover cookies.

Mathematicians care about divisibility because it reveals patterns in numbers. Every even number is divisible by 2. Numbers ending in 0 or 5 are divisible by 5. A number is divisible by 3 if its digits add up to a number divisible by 3 (for example, 27 works because 2 + 7 = 9, and 9 is divisible by 3).

Understanding divisibility helps you work with fractions, find common denominators, and solve all sorts of mathematical problems.