Determining the factor pairs of the number fifteen involves identifying two integers that, when multiplied together, produce the result of fifteen. For example, one such pair is 3 and 5, as 3 multiplied by 5 yields 15. Additionally, 1 and 15 constitute another valid pair, since 1 multiplied by 15 also equals 15. Negative integers can also be considered; thus, -3 and -5, as well as -1 and -15, also fulfill this criterion.
Understanding the composition of a number through its factors is fundamental in various mathematical operations. This knowledge is essential for simplifying fractions, solving algebraic equations, and grasping concepts related to divisibility. Historically, the ability to decompose numbers into their constituent factors has been critical in fields such as accounting, engineering, and cryptography, where precise calculations are paramount.