📚 Understanding Divisibility Rules for 2, 5, and 10
Divisibility rules are shortcuts to check if a number can be divided evenly by another number, without actually doing the division! Let's see why the rules for 2, 5, and 10 work.
- 🔢 Divisibility by 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8). Think of any number as being made up of tens and ones. For example, $36 = (3 \times 10) + 6$. Since 10 is divisible by 2, any multiple of 10 is also divisible by 2. So, whether the whole number is divisible by 2 depends only on whether that last digit (the ones place) is divisible by 2.
- 🖐️ Divisibility by 5: A number is divisible by 5 if its last digit is a 0 or a 5. Similar to the rule for 2, we can represent a number like this: $75 = (7 \times 10) + 5$. Because 10 is divisible by 5, any multiple of 10 is also divisible by 5. So, the divisibility of the whole number by 5 depends only on the divisibility of the last digit by 5.
- 🔟 Divisibility by 10: A number is divisible by 10 if its last digit is 0. This is the easiest one! Again, think of a number like this: $120 = (12 \times 10) + 0$. Since the number is made up of some multiple of 10, plus the last digit, and the last digit has to be zero to make the *entire* number a multiple of 10. If the last digit is *any* other number, it *won't* be divisible by 10.
➕ Examples
- ✔️ Example for 2: 48 is divisible by 2 because 8 is even.
- ✔️ Example for 5: 95 is divisible by 5 because it ends in 5.
- ✔️ Example for 10: 230 is divisible by 10 because it ends in 0.
✍️ Practice Quiz
Determine if each number is divisible by 2, 5, or 10.
- Is 34 divisible by 2, 5, or 10?
- Is 75 divisible by 2, 5, or 10?
- Is 120 divisible by 2, 5, or 10?
- Is 22 divisible by 2, 5, or 10?
- Is 45 divisible by 2, 5, or 10?
- Is 100 divisible by 2, 5, or 10?
- Is 68 divisible by 2, 5, or 10?