Finding New Factors with the Associative Property
This Grade 4 Eureka Math skill teaches students to discover new factors of a number by grouping its prime or known factors using the associative property. If a number equals a × b × c, then any product of two of those factors — like (a × b) — is also a factor. For example, since 30 = 2 × 3 × 5, students find that 6, 10, and 15 are factors by grouping pairs. This systematic approach, covered in Chapter 14 of Eureka Math Grade 4, gives students a powerful strategy for finding all composite factors of a number.
Key Concepts
If a number is expressed as a product of factors, you can multiply those factors together in groups to find new factors. If $N = a \times b \times c$, then the product $(a \times b)$ is also a factor of $N$.
Common Questions
How does the associative property help find new factors?
By regrouping the known factors of a number, you can multiply pairs together to reveal new composite factors. For example, from 2 × 3 × 5 = 30, grouping (2×3)=6 shows that 6 is also a factor of 30.
What is a factor of a number?
A factor is a whole number that divides evenly into another number with no remainder. For example, 6 is a factor of 30 because 30 ÷ 6 = 5 with remainder 0.
How do you find all factors of 54 using this method?
Write 54 as a product: 54 = 2 × 3 × 9. Then group pairs: (2×3)=6 and (3×9)=27. So 6 and 27 are additional factors of 54.
What is the difference between prime factors and composite factors?
Prime factors are factors that are prime numbers (like 2, 3, 5). Composite factors are products of two or more prime factors, such as 6 (=2×3) or 15 (=3×5).
Can this method find all factors of a number?
Systematic grouping of all prime factor combinations will produce all composite factors. Combine each possible pair and triple from the prime factorization to build a complete factor list.