Prime Time Unit Test Study Guide- Answers and Review

What This Guide Covers

You're here because you need to actually understand Prime Time material, not just memorize it. This guide gives you the answers you need plus the reasoning behind them. No padding, no motivational garbage.

Prime Time is typically a unit about factors, multiples, primes, and divisibility. If that's your unit, you're in the right place.

Core Concepts You Must Know

Factors vs. Multiples

This trips up more students than you'd think. Get it straight now.

• A factor goes into a number evenly. Example: 3 is a factor of 12 because 12 ÷ 3 = 4 with no remainder.
• A multiple is what you get when you multiply. Example: 12 is a multiple of 3 because 3 × 4 = 12.

Simple rule: factors are inside the number, multiples are outside the number.

Prime Numbers

A prime number has exactly two factors: 1 and itself. That's it.

The primes under 20: 2, 3, 5, 7, 11, 13, 17, 19

Know this cold. You'll use primes constantly in this unit.

Greatest Common Factor (GCF)

The GCF is the largest number that divides into two or more numbers. Find it by listing factors or using prime factorization.

Example: GCF of 24 and 36

• Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
• Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
• Common factors: 1, 2, 3, 4, 6, 12
• GCF = 12

Least Common Multiple (LCM)

The LCM is the smallest number that two or more numbers divide into evenly.

Example: LCM of 4 and 6

• Multiples of 4: 4, 8, 12, 16, 20...
• Multiples of 6: 6, 12, 18, 24...
• First common multiple: 12
• LCM = 12

Common Types of Problems

Word Problem Strategy

Most students lose points on word problems because they don't identify whether they need GCF or LCM.

GCF situations: Sharing items into equal groups with nothing left over. Cutting things into largest equal pieces. Grouping.

LCM situations: Events that repeat on schedules. Finding when things align. Packaging problems.

Ask yourself: "Am I dividing up (GCF) or finding when things happen together (LCM)?"

Practice Problems with Answers

1. Is 27 prime or composite?

Composite. It has factors 1, 3, 9, and 27.

2. Find the GCF of 45 and 60.

Factors of 45: 1, 3, 5, 9, 15, 45

Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

GCF = 15

3. Find the LCM of 8 and 12.

Multiples of 8: 8, 16, 24, 32...

Multiples of 12: 12, 24, 36...

LCM = 24

4. Two bells ring every 6 and 8 seconds. When do they ring together?

Find LCM of 6 and 8 = 24 seconds

5. You have 24 apples and 36 oranges. What's the largest number of baskets with equal fruit, no mixing?

Find GCF of 24 and 36 = 12 baskets

Where Students Lose Points

• Confusing GCF and LCM — Double-check which one the problem asks for
• Missing factors — Work in pairs to avoid skipping numbers
• Rushing on primes — 1 is NOT prime. 2 is the only even prime
• Not showing work — Even if you know the answer, the process matters
• Arithmetic errors — Basic multiplication/division mistakes sink grades

How to Study Effectively

Day Before the Test

• Redo homework problems you got wrong
• Practice 5-10 GCF/LCM problems without notes
• Recite the primes under 30 until it's automatic

Night Before

• Get actual sleep. Cramming math at midnight is useless.
• Look at one practice test, don't try to relearn everything

Morning of the Test

• Read each word problem twice before solving
• Underline whether it asks for GCF or LCM
• Show your work even on easy problems
• Check your division by multiplying back

Quick Reference Cheat Sheet

• Prime = 2 factors only
• Composite = more than 2 factors
• 1 is neither prime nor composite
• 2 is the only even prime
• GCF = biggest shared factor = dividing up
• LCM = smallest shared multiple = scheduling

If you know these distinctions and can apply them to word problems, you're set. Don't overthink this unit. It's about patterns, and patterns are learnable.