SAT Math · Study & Practice
Factors and Multiples
Factors and multiples underpin a large share of SAT number questions — primes, GCF/LCM word problems, divisibility shortcuts and prime factorization all live here. Work through each topic, try the unsolved problems with the hint ladder, then take the 8-question topic test.
Topics
1
Prime Numbers
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2
Composite Numbers
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3
Prime Factorization
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4
Greatest Common Factor (GCF)
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5
Least Common Multiple (LCM)
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6
Divisibility Rules
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7
Factor Trees
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Chapter test
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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