Defining a Multiple
Defining a Multiple is a Grade 4 math skill that introduces the concept of a multiple as the product you get when you multiply a given number by any whole number (1, 2, 3, 4, ...). The multiples of 4 are 4, 8, 12, 16, 20, and so on. Every number has infinitely many multiples. Covered in Chapter 7: Factors and Multiples in Eureka Math Grade 4, understanding multiples is foundational for finding the least common multiple (LCM), adding fractions with unlike denominators, skip-counting patterns, and divisibility — all skills that build in 5th and 6th grade.
Key Concepts
A whole number $b$ is a multiple of another whole number $a$ if $b$ can be obtained by skip counting by $a$, or equivalently, if $b \div a$ results in a whole number (a remainder of 0). This relationship can be expressed as $b = n \times a$, where $n$ is a non zero whole number.
Common Questions
What is a multiple in math?
A multiple of a number is the result of multiplying that number by any whole number. For example, multiples of 5 are 5, 10, 15, 20, 25, ... (5 x 1, 5 x 2, 5 x 3, ...). Every whole number has infinitely many multiples.
What are the first five multiples of 6?
The first five multiples of 6 are 6, 12, 18, 24, and 30 — calculated as 6 x 1, 6 x 2, 6 x 3, 6 x 4, and 6 x 5. Multiples of 6 are all even and include 6 as a factor.
What is the difference between a factor and a multiple?
A factor of a number divides into it evenly. A multiple of a number is the result of multiplying it by a whole number. For 12: factors are 1, 2, 3, 4, 6, 12; multiples are 12, 24, 36, 48, ... Factors are smaller; multiples are larger or equal.
Is every number a multiple of itself?
Yes. Every number n is a multiple of itself because n x 1 = n. The first multiple in any sequence is the number itself. A number is also a multiple of 1 (since n = 1 x n) and a multiple of every factor it has.
How do multiples connect to skip counting?
Skip counting by a number generates that number's multiples. Counting by 3s gives 3, 6, 9, 12, ... which are the multiples of 3. Understanding skip counting provides a mental shortcut for listing multiples quickly.
What chapter in Eureka Math Grade 4 covers multiples?
Chapter 7: Factors and Multiples in Eureka Math Grade 4 covers the definition of multiples, skip counting to list multiples, identifying multiples of given numbers, and connecting multiples to the concept of common multiples for fraction work.