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➕pre-algebra review

Factor Pairs

Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025

Definition

Factor pairs refer to the combinations of two numbers that, when multiplied together, result in a given product. They represent the different ways a number can be expressed as the product of two factors.

5 Must Know Facts For Your Next Test

  1. Factor pairs are important in finding all the factors of a number, which is a key concept in the context of finding multiples and factors.
  2. The number of factor pairs for a given number is determined by the number of positive divisors of that number.
  3. For prime numbers, the only factor pairs are 1 and the number itself, as prime numbers have no other positive divisors.
  4. The sum of the factors in a factor pair is always equal to the number being factored plus 1.
  5. Identifying factor pairs can be useful in simplifying expressions, solving equations, and understanding number properties.

Review Questions

  • Explain how factor pairs relate to finding the factors of a number.
    • Factor pairs represent the different ways a number can be expressed as the product of two factors. By identifying all the factor pairs of a number, you can determine all the positive factors of that number. This is an important step in the process of finding multiples and factors, as the factors of a number are the building blocks for generating its multiples.
  • Describe the relationship between the sum of the factors in a factor pair and the number being factored.
    • The sum of the two factors in a factor pair is always equal to the number being factored plus 1. For example, if the number being factored is 6, the factor pairs are 1 and 6, 2 and 3, and the sum of the factors in each pair is 7 (1 + 6 = 7, 2 + 3 = 7). This pattern holds true for any number, and it can be a useful way to identify and verify factor pairs.
  • Analyze how the number of factor pairs for a number is related to the number of positive divisors of that number.
    • The number of factor pairs for a given number is directly related to the number of positive divisors of that number. This is because each factor pair represents a unique way to express the number as a product of two factors, and each of those factors is also a positive divisor of the number. For example, the number 12 has four positive divisors (1, 2, 3, 4, 6, 12), and it also has four factor pairs (1 and 12, 2 and 6, 3 and 4). This relationship can be used to efficiently determine all the factors of a number by identifying its factor pairs.