← 7th Grade Math
Math 7 U4-L2 Patterns and Number Sense

Prime Factorization

Every number bigger than 1 is either a prime or a stack of primes multiplied together. Breaking a number down into its primes is like taking apart a machine to see what it's made of.

Teacher Notes

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Lesson Goal

By the end of this lesson your student should be able to tell a prime from a composite number, and write the prime factorization of a composite number with a factor tree or by dividing by the least prime, using exponents for repeats.

Where Students Get Stuck

🚨 Calling 1 a prime. A prime needs exactly two factors, and 1 only has one, so 1 is neither prime nor composite.

Stopping a factor tree too early, with a composite number like 4 or 10 still sitting at the end of a branch.

Thinking different trees give different answers. They look different and always end in the same primes.

Teaching Suggestion

Have the student multiply the primes back together at the end of every problem. If the product doesn't match the number he started with, a prime went missing.

Key Vocabulary

Prime
A whole number greater than 1 with exactly two factors, 1 and itself.
Composite
A whole number greater than 1 with more than two factors.
Factor tree
A diagram that splits a number into factors, then splits each factor, until every branch ends in a prime.
Prime factorization
A number written as a product of primes, such as 12 = 2 × 2 × 3.
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Before You Start

The Words

The words this lesson uses. Tap a card to see what it means, then come back to them whenever a question uses one.

Part One

The Questions

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Questions about the story you just read. Pick your answer straight off, or press Find it in the story if you would rather hunt for the sentence first.

Part Two

Vocabulary Check

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The word cards are at the top of this page. Look back at them as often as you need, then answer.

When you finish: write the answers out in your own words — not copied word for word from the choices. Saying it your own way is the part that proves you understood it. Then use Print Answer Sheet for a one-page record of what was answered and scored.
Open The Homework SheetDo it on screen or print it. Your score shows here once you check it.