The lesson

This lesson teaches Factors, Multiples, GCF & LCM. Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.

Factors and multiples

A factor is a number that divides evenly into another number, leaving no remainder. The factors of 12 are 1, 2, 3, 4, 6, and 12, because each one divides 12 exactly.

A multiple is what you get when you skip-count by a number. The multiples of 4 are 4, 8, 12, 16, 20, and so on. Notice that every number is a factor of its own multiples.

A quick way to test factors: divide the number by each candidate. If the quotient is a whole number with no remainder, you found a factor.

Every whole number has at least two factors: 1 and itself. Prime numbers have exactly those two, which is why primes are the building blocks for bigger numbers.

Greatest Common Factor (GCF)

The GCF of two numbers is the largest factor they share. List the factors of each number, then pick the biggest one that appears in both lists.

A quick way to test factors: divide the number by each candidate. If the quotient is a whole number with no remainder, you found a factor.

Every whole number has at least two factors: 1 and itself. Prime numbers have exactly those two, which is why primes are the building blocks for bigger numbers.

Find the GCF of 18 and 24.

1Factors of 18: 1, 2, 3, 6, 9, 18
2Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
3Shared factors: 1, 2, 3, 6 - the greatest is 6.

Least Common Multiple (LCM)

The LCM is the smallest multiple that two numbers share. Skip-count by each number until you reach the first value they both land on.

Multiples never end. You can always keep skip-counting. The first multiple of any number (except 0) is the number itself.

When a word problem asks when two events happen together again, you are usually looking for a common multiple, often the least common multiple (LCM).

Find the LCM of 6 and 8.

1Multiples of 6: 6, 12, 18, 24, 30…
2Multiples of 8: 8, 16, 24, 32…
3First match: 24.

Why this matters

Factors, Multiples, GCF & LCM shows up constantly in numbers that divide evenly, numbers you count by, and the values they share. It also connects to what you will see on homework, quizzes, and the next unit in this grade.

Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.

Common mistakes to avoid

Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.

Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.

Key ideas from this lesson

Factors and multiples
Greatest Common Factor (GCF)
Least Common Multiple (LCM)

Video walkthrough

Math Antics

Prime Factorization

Break any number into its prime building blocks - the key to GCF and LCM.

Watch on YouTube

Practice

For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.

Exercise 1

Try it yourself

List all the factors of 24.