Quick Answer
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.
A factor of an integer n is any integer d such that n divided by d results in another integer. In mathematical terms, if a × b = c, then both a and b are factors of c.
Question: If x is a factor of 42 and x is a prime number, which of the following could be the value of x? (A) 4 (B) 6 (C) 7 (D) 9. Solution: The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. Among these, the prime factors are 2, 3, and 7. Since 7 is the only option listed that is both a factor and prime, the correct answer is (C).
Confusing factors with multiples: Students often mix these up, thinking that a factor of 6 is 12, when 12 is actually a multiple.
Forgetting the number 1 and the number itself: Every integer n has at least 1 and n as factors, which are often overlooked in counting problems.
Neglecting negative factors: While less common on the SAT, factors can technically be negative integers, such as -2 being a factor of 4.
Students targeting 750+ should know that the number of factors an integer has can be determined by adding one to each exponent in its prime factorization and multiplying those results together.
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.
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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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.