When you’re learning about factors and multiples in Year 7 math, it’s important to know how they are different, even though people often use the terms like they mean the same thing. Let's break it down so it's easier to understand.

What Are Factors?

Factors are numbers that you can divide into another number without leaving any leftover.

In simpler terms, if you can multiply two whole numbers together to get a specific number, then those two numbers are called factors of that number.

Example: For the number 12, here are its factors:

• 1 (because $1 \times 12 = 12$)
• 2 (because $2 \times 6 = 12$)
• 3 (because $3 \times 4 = 12$)
• 4
• 6
• 12

So, the numbers that can divide 12 evenly are its factors. If you’re unsure, you can just write them down to check!

What Are Multiples?

Multiples are what you get when you multiply a number by whole numbers. You can think of it like counting by that number.

Example: For the number 3, the first few multiples are:

• $3 \times 1 = 3$
• $3 \times 2 = 6$
• $3 \times 3 = 9$
• $3 \times 4 = 12$
• $3 \times 5 = 15$

So, the multiples of 3 are 3, 6, 9, 12, 15, and so on. You keep adding 3 each time.

Key Differences

• Nature: Factors are about dividing, while multiples are about multiplying.

• Set Size: Every number has only a few factors (like 1, 2, 3, ...), but it has endless multiples (3, 6, 9, ... going on forever).

• How to Find Them: You find factors by checking which numbers can divide the main number without leftovers. You find multiples by multiplying the number by whole numbers.

Visualizing It

You can think of factors like puzzle pieces that fit perfectly into your number. In contrast, multiples are like endless lines on a number line. Both factors and multiples are important because they help you understand more complex math topics like fractions, ratios, and prime numbers!

Understanding these differences will not only help you in Year 7 math but also get you ready for algebra and more!