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.
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.
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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.