Quick Answer
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 prime number is any natural number n > 1 that cannot be formed by multiplying two smaller natural numbers. Mathematically, its only divisors are the set {1, n}.
Question: If x is a prime number such that 10 < x < 20, and x + 2 is also a prime number, what is one possible value of x? Solution: The primes between 10 and 20 are 11, 13, 17, and 19. Checking x + 2: 11 + 2 = 13 (prime) 13 + 2 = 15 (not prime) 17 + 2 = 19 (prime) 19 + 2 = 21 (not prime) Thus, x could be 11 or 17.
Mistaking 1 for a prime number: Students often forget that 1 is neither prime nor composite by definition.
Assuming all odd numbers are prime: Many students incorrectly categorize numbers like 9, 15, or 21 as prime simply because they are odd.
Overlooking 2: Students frequently forget that 2 is the only even prime number, which is a common 'trap' in SAT constraint problems.
Students targeting 750+ should know that the prime factorization of a number determines the total number of its factors; if a number n = p^a * q^b, the total number of factors is (a+1)(b+1), a shortcut often useful for high-difficulty divisor questions.
Composite Number
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.
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.
A prime number on the SAT is a whole number greater than 1 that has no divisors other than 1 and itself. It appears as a fundamental concept in the Math section, often used to define variables in algebraic expressions or to test a student's ability to manipulate integers and factors within both modules of the exam.
To identify a prime number, check if it is divisible by any prime numbers less than its square root. On the SAT, you should memorize primes up to 20. For larger numbers, use the divisibility rules for 2, 3, and 5 to quickly eliminate most composite candidates during the timed Math modules.
The difference between a prime number and a composite number lies in their factor count. A prime number has exactly two factors (1 and itself), whereas a composite number has more than two factors. Note that 1 is neither prime nor composite, a distinction occasionally tested in SAT number property questions.
Prime numbers typically appear in approximately 1 to 3 questions per Digital SAT exam. These questions usually integrate prime properties into broader topics like factoring or exponent rules, requiring students to apply their knowledge of primes to narrow down possible integer solutions in the Math section.
