ACT Math Pre-Algebra Integers and Number Properties Factors Multiples Primes

Pre-Algebra — Integers and Number Properties: Factors, Multiples, Primes

What This Is and Why It Matters for the ACT

Pre-Algebra is a fundamental math concept that appears in the ACT Math section. It's a crucial topic that helps you solve equations, inequalities, and functions. You'll encounter questions on factors, multiples, primes, and number properties. These questions can be challenging, but with practice and understanding, you can master them.

Key Concepts (What You Must Know)

• Definition: An integer is a whole number, either positive, negative, or zero.
• Factors: A factor of a number is a whole number that divides the number without leaving a remainder.
• Multiples: A multiple of a number is the product of that number and an integer.
• Primes: A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself.
• Properties of integers: Integers have properties such as commutativity, associativity, and distributivity.

Step-by-Step Strategy for This Topic

1. Read the question carefully: Understand what's being asked and what information is given.
2. Identify the key elements: Look for factors, multiples, primes, or number properties mentioned in the question.
3. Eliminate wrong answers: Use your knowledge of factors, multiples, primes, and number properties to eliminate answer choices that are clearly incorrect.
4. Check your work: Verify your answer by plugging it back into the question or using a calculator (if allowed).
5. Time management: Allocate 1-2 minutes per question, depending on the complexity.

⚠️ Common mistake: Assuming a number is prime without checking its divisors.

How It’s Tested on the ACT

• Math: Multiple-choice questions with five answer choices.
• Common distractors: Answer choices that are close to the correct answer but not exactly correct.
• Tips: Use your knowledge of factors, multiples, primes, and number properties to eliminate answer choices.

Common Mistakes & Exam Traps

1. The mistake: Assuming a number is prime without checking its divisors.
   • Why it happens: Rushing through the question or not checking the number's divisors.
   • How to avoid it: Take your time and check the number's divisors before assuming it's prime.
   • Exam board insight: The ACT examiners penalize incorrect assumptions about prime numbers.
2. The mistake: Not considering all possible factors of a number.
   • Why it happens: Not reading the question carefully or not considering all possible combinations.
   • How to avoid it: Read the question carefully and consider all possible combinations of factors.
   • Exam board insight: The ACT examiners expect you to consider all possible factors of a number.
3. The mistake: Not using the correct formula for finding multiples or factors.
   • Why it happens: Not memorizing the formulas or not applying them correctly.
   • How to avoid it: Memorize the formulas and apply them correctly.
   • Exam board insight: The ACT examiners expect you to use the correct formulas for finding multiples or factors.
4. The mistake: Not checking the answer choices for prime numbers.
   • Why it happens: Not reading the question carefully or not checking the answer choices.
   • How to avoid it: Read the question carefully and check the answer choices for prime numbers.
   • Exam board insight: The ACT examiners penalize incorrect assumptions about prime numbers.

Practice Questions (3-5 questions)

Question 1:
What is the greatest common factor of 12 and 18? A) 2 B) 3 C) 6
D) 9 E) 12

Answer: C) 6
Explanation: The greatest common factor of 12 and 18 is 6, since 6 is the largest number that divides both 12 and 18 without leaving a remainder.

Question 2:
What is the least common multiple of 4 and 6? A) 12 B) 18 C) 24
D) 36 E) 48

Answer: C) 24
Explanation: The least common multiple of 4 and 6 is 24, since 24 is the smallest number that is a multiple of both 4 and 6.

Question 3:
Is the number 27 a prime number? A) Yes B) No C) Maybe D) It depends E) Unknown

Answer: B) No Explanation: The number 27 is not a prime number, since it has divisors other than 1 and itself (3 and 9).

Quick Reference Card (60-Second Summary)

• Factors: A factor of a number is a whole number that divides the number without leaving a remainder.
• Multiples: A multiple of a number is the product of that number and an integer.
• Primes: A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself.
• Properties of integers: Integers have properties such as commutativity, associativity, and distributivity.
• Greatest common factor (GCF): The GCF of two numbers is the largest number that divides both numbers without leaving a remainder.
• Least common multiple (LCM): The LCM of two numbers is the smallest number that is a multiple of both numbers.

If You Get Stuck on Test Day

• What to do when you don't know the answer: Eliminate answer choices that are clearly incorrect and make an educated guess.
• Pacing strategy: Allocate 1-2 minutes per question, depending on the complexity.
• When to skip and come back: If you're stuck on a question, skip it and come back to it later.

Related ACT Topics

• Factors and multiples: Understanding factors and multiples is crucial for solving equations and inequalities.
• Prime numbers: Prime numbers are essential for understanding number properties and algebraic expressions.
• Number properties: Number properties, such as commutativity and associativity, are essential for understanding algebraic expressions.