Understanding Factors In Mathematics
Factors As Building Blocks
Factors are numbers that, when multiplied, form a product. In 2 x 3 = 6, 2 and 3 are factors, and 6 is the product.
When students understand factors, they build fluency in basic operations and lay the groundwork for more advanced concepts, such as prime factorization and greatest common factors. This foundational knowledge is essential for skills like simplifying fractions and solving problems involving ratios.
The Role Of Factors In Multiplication And Division
Division and multiplication are inverse operations. A factor of a multiplication problem is the divisor in its related division problem. For example, as we saw earlier, in 2 x 3 = 6, 2 and 3 are factors, and 6 is the product. In its related division problems we see 6 ÷ 2 = 3 and 6 ÷ 3 =2.
This connection helps students develop fact fluency and provides a practical way to check their work. Using fact families, students can see how multiplication and division interact, reinforcing their understanding of factors.
Note on Prime Factors
Factors can include both prime and composite numbers. Prime factorization is a process where a number is expressed as a product of its prime factors. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, while its prime factorization is 2 × 2 × 3.
Teaching Strategies For Factors
Visualizing Factors With Arrays And Area Models
Arrays and area models make the role of factors explicit by organizing numbers into rows and columns. In these models, the rows and columns represent the factors of a number, while the total number of objects represents the product. This visualization helps students see how factors work together to form a product in multiplication and how they break the product into equal groups in division.
For example, to explore the factors of 12, students can create a 4×3 array:
- The rows (4) and columns (3) are the factors, and the total number of objects (12) is the product.
- When used for division, the same array shows 12 ÷ 4 = 3 (12 objects grouped into 4 rows) and 12 ÷ 3 = 4 (12 objects grouped into 3 columns).
