Module 1 · Numbers and Operations
Chapter 2: Factors and Multiples
Math Foundations
7 topics
🎯 150 practice questions
What this chapter covers
The 7 topics below make up Factors and Multiples on the Digital SAT. Click any topic to open its notes, examples and practice test.
1Prime Numbers
2Composite Numbers
3Prime Factorization
4Greatest Common Factor (GCF)
5Least Common Multiple (LCM)
6Divisibility Rules
7Factor Trees
Study material & tests
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Notes, worked examples and hint-guided practice for every topic.
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🎯 Topic tests
8 auto-graded questions per topic, pulled from the question bank.
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25 fresh mixed-difficulty questions, timed, with full solutions.
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Formula Reference Sheet
This chapter
Divisibility rules
| by 2 | last digit is even |
|---|---|
| by 3 | digit sum divisible by 3 |
| by 4 | last two digits divisible by 4 |
| by 5 | ends in 0 or 5 |
| by 6 | divisible by 2 and 3 |
| by 8 | last three digits divisible by 8 |
| by 9 | digit sum divisible by 9 |
| by 10 | ends in 0 |
| by 11 | alternating digit sum divisible by 11 |
Factors, GCF & LCM
| GCF × LCM | GCF(a,b) × LCM(a,b) = a × b |
|---|---|
| Number of divisors | if n = p^a · q^b · …, count = (a+1)(b+1)… |
| GCF from primes | product of shared primes to the LOWEST power |
| LCM from primes | product of all primes to the HIGHEST power |
| Coprime | GCF(a,b) = 1 |
| Perfect square | every prime exponent is even |
Primes
| Definition | exactly two factors: 1 and itself |
|---|---|
| Only even prime | 2 |
| Primality test | no prime ≤ √n divides n ⇒ n is prime |
Digital SAT reference
Area & Circumference
| Circle area | A = πr² |
|---|---|
| Circle circumference | C = 2πr |
| Rectangle | A = ℓw |
| Triangle | A = ½ b h |
Volume
| Rectangular box | V = ℓwh |
|---|---|
| Cylinder | V = πr²h |
| Sphere | V = 4⁄3 πr³ |
| Cone | V = 1⁄3 πr²h |
| Pyramid | V = 1⁄3 ℓwh |
Right triangles
| Pythagorean theorem | a² + b² = c² |
|---|---|
| 30°–60°–90° | sides x : x√3 : 2x |
| 45°–45°–90° | sides s : s : s√2 |
Constants
| Degrees in a circle | 360° |
|---|---|
| Radians in a circle | 2π |
| Angles of a triangle | sum = 180° |
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