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.
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.
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 factor is an integer that divides into another integer with no remainder. On the Digital SAT, factors are used to simplify algebraic expressions and solve quadratic equations. Understanding factors is essential for identifying the zeros of a function and is typically tested in the Math section across both modules as a foundational arithmetic and algebraic skill.
To identify a factor of a number, divide the number by potential integers starting from 1. If the result is a whole number without a remainder, that divisor is a factor. For larger numbers on the SAT, use prime factorization or the divisibility rules for 2, 3, 5, and 10 to quickly find smaller components.
A factor is a number that divides into a larger number, whereas a multiple is the product of a number and an integer. For example, 3 is a factor of 12 because 12 divided by 3 is 4; conversely, 12 is a multiple of 3 because 3 times 4 is 12.
Typically, you might encounter approximately 2 to 5 questions that directly or indirectly test factors on a single Digital SAT. These questions often appear in the context of polynomial factoring, finding common denominators, or solving word problems involving divisibility. Mastery of factors is often a prerequisite for solving more advanced math problems.
