Write a definition for factor pairs then give an example
The correct answer and explanation is:
Factor Pairs:
Factor pairs are two numbers that, when multiplied together, yield a given product. These numbers are considered factors of the product. Factor pairs are essentially different combinations of two factors that, when multiplied, give the original number. Every whole number has at least one pair of factors, and many numbers have multiple pairs.
Example:
Consider the number 12. The factor pairs of 12 are:
- (1, 12)
- (2, 6)
- (3, 4)
Each of these pairs multiplies to give the product 12, so they are all factor pairs of the number 12.
Explanation:
Understanding factor pairs is important for various mathematical tasks, especially when working with prime factorization, simplification of fractions, or finding common divisors. Factor pairs can help in determining the divisibility of a number and understanding its structure. For instance, finding the factors of a number is a common step in solving problems related to greatest common divisors (GCD) or least common multiples (LCM).
When a number is factored into two smaller numbers, those two numbers are called factor pairs. The factors of a number are always positive integers (whole numbers). A unique characteristic of factor pairs is that one of the numbers is always smaller than or equal to the square root of the original number, while the other is larger than or equal to the square root. For example, for 12, the square root is approximately 3.46, so the factor pair (3, 4) fits this rule since 3 is less than 3.46 and 4 is greater than 3.46.
The process of finding factor pairs is an essential concept in number theory, and it is often used to simplify problems in algebra, geometry, and other areas of mathematics. Understanding how to find factor pairs helps students develop a deeper understanding of numbers and their relationships to each other.