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.
Factor (Number)
A factor is an integer that divides another integer perfectly without leaving a remainder. On the Digital SAT, factors appear frequently in Math Modules 1 and 2, often within algebraic simplification or polynomial questions. Typically, students must identify factors to find roots or simplify expressions, making this concept vital for a high score.
Factoring
Factoring is the mathematical process of breaking down a polynomial into a product of simpler expressions or factors. On the Digital SAT, this technique is frequently tested in the Math modules, appearing in approximately 10-15% of algebra and advanced math questions, often requiring students to identify equivalent expressions or find the zeros of quadratic functions.
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.
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.
A composite number on the SAT is any positive integer greater than 1 that possesses more than two factors. Unlike prime numbers, which only have two factors (1 and itself), composite numbers can be divided evenly by other integers. They appear in both Math modules, often as a constraint in word problems or algebraic equations involving integer properties.
To identify a composite number, check if the integer is greater than 1 and has any divisors other than 1 and itself. You can use divisibility rules (like checking if the sum of digits is divisible by 3) or perform prime factorization. If the number has at least three distinct factors, it is classified as a composite number.
The primary difference lies in the number of factors: prime numbers have exactly two distinct factors (1 and the number itself), while composite numbers have three or more. For example, 7 is prime because its only factors are 1 and 7, whereas 8 is composite because its factors are 1, 2, 4, and 8.
While questions solely asking for a definition are rare, approximately 5% to 10% of the Math section involves number properties where composite numbers play a role. They typically appear as part of larger problems involving factors, multiples, or remainders, requiring students to apply the definition to narrow down possible integer values for variables.
