Multiples & Factors

Multiples vs. Factors — What's the Difference?

∞ Multiples

Multiples of a number are made by multiplying that number by any whole number. Every number has an infinite number of multiples — they go on forever!

Multiples of 2:
2×1 = 2
2×2 = 4
2×3 = 6
2×4 = 8
2×5 = 10 ... and on forever!

∞ All numbers have an INFINITE number of multiples

√ Factors

Factors are the numbers you multiply together to get a number. Every number has a fixed number of factors — you can list them all!

Factors of 48:
1 × 48 = 48
2 × 24 = 48
3 × 16 = 48
4 × 12 = 48
6 × 8 = 48

✓ All numbers have a FIXED number of factors

Memory Hint: Think of Multiples as going Many places (infinite!) and Factors as being Few (a fixed set). This same hint helps with GCF and LCM later!

Factor Finder

Type any number and find all of its factors instantly!

Find factors of:

Try these: Factors of 36 | Factors of 48 | Factors of 100 | Factors of 60

GCF & LCM with a Venn Diagram

Using the prime factorizations from the factor trees above: 18 = 2 × 3 × 3 and 24 = 2 × 2 × 2 × 3

Click each prime factor in the bank below, then click where it belongs in the Venn diagram!

Only in 18 (left)

Both (middle)

Only in 24 (right)

Prime Factor Bank — click a factor, then click where it goes:

3 (from 18)

2 (from 24)

2 (shared)

3 (shared)

Practice Problems

Choose a set and check your answers!

Find the 5th multiple of each number.

How many factors does each number have?

Find the Greatest Common Factor of each pair.

Find the Least Common Multiple of each pair.

Teaching Ideas

🎮 Factor Game

Students take turns choosing numbers from a grid. Their score is the sum of all factors of that number not yet claimed. The player with the highest score wins. This builds factor fluency in a competitive, engaging way.

🍔 Real World LCM

Use the hot dog and bun problem as an introduction. Then have students find their own real-world LCM problems — items that come in different-sized packages that they'd want equal amounts of.

🔗 Fraction Connection

Immediately connect GCF to simplifying fractions and LCM to finding common denominators. Students understand the purpose better when they see how these skills are used in the very next lesson.

📊 Color-Coded Venn Diagrams

Have students use three colors — one for each section of the Venn diagram. The overlap color reminds them that shared factors go in the GCF calculation, while all colors together form the LCM.

✏ Interactive Notebook Foldables

The downloadable foldables work beautifully in interactive notebooks. The two-pocket design for Multiples and Factors lets students store their own examples, making it a personalized reference tool.

🔍 Divisibility Rules Connection

Teach divisibility rules for 2, 3, and 5 alongside factor trees. Students who know that a number is divisible by 3 if its digits sum to a multiple of 3 will build factor trees much more efficiently.

Multiples vs. Factors — What's the Difference?

∞ Multiples

√ Factors

Explore Multiples

Factor Finder

Factor Trees — Step by Step

GCF & LCM with a Venn Diagram

Calculate GCF & LCM:

The List Method for GCF & LCM

Greatest Common Factor (GCF)

Least Common Multiple (LCM)

🍔 Real World Problem — Hot Dogs & Buns!