Quick Answer
A composite number is a positive integer greater than 1 that has more than two distinct factors. On the Digital SAT, these appear typically in Math Module 1 or 2 within number theory or factoring questions. Understanding them is crucial for identifying prime versus non-prime options in multiple-choice questions about integer properties.
A composite number is a positive integer $n > 1$ that is not prime, meaning it has at least one divisor other than 1 and itself. Mathematically, it can be expressed as $n = a \times b$ where $1 < a, b < n$.
Question: If $x$ is the smallest composite number and $y$ is the smallest prime number, what is the value of $2x + 3y$? Solution: The smallest composite number is 4 (factors: 1, 2, 4). The smallest prime number is 2. Therefore, $2(4) + 3(2) = 8 + 6 = 14$.
Confusing 1 as a composite number: Students often forget that 1 is neither prime nor composite, as it only has one factor.
Assuming all even numbers are composite: While almost all even numbers are composite, 2 is the only even prime number.
Misidentifying odd numbers as prime: Students may assume odd numbers like 9, 15, or 21 are prime, forgetting they have factors other than 1 and themselves.
Students targeting 750+ should know that the product of any two prime numbers is always a composite number with exactly three or four factors, which is a useful shortcut for analyzing integer properties in advanced polynomial or number theory problems.
Integer
An integer is a whole number that can be positive, negative, or zero. On the Digital SAT, integers appear frequently across both Math modules, particularly in student-produced response questions where answers must often be non-decimal. Mastering integers is essential for solving approximately 15-20% of algebraic and data analysis problems.
Multiple
A multiple is the product of any integer and another integer. On the Digital SAT, multiples appear frequently in Math Modules 1 and 2, often within word problems involving cycles or sequences. Typically, students must calculate the Least Common Multiple (LCM) to solve problems concerning synchronized events or common denominators.
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Prime Number
A prime number is a positive integer greater than 1 with exactly two distinct factors: 1 and itself. On the Digital SAT, prime numbers frequently appear in Math Module 1 and 2 within Number Properties or Algebra questions. Students typically encounter at least one question involving prime factorization or integer constraints per test.