Finding the Factor Pairs of 91 1 91 2 45.5 3 30.3333 4 22.75 5 18.2 6 15.1667 7 13 8 11.375 9 10.1111 91 is a composite number. 91 = 1 x 91 or 7 x 13. Factors of 91: 1, 7, 13, 91. Prime factorization: 91 = 7 x 13. 16 Apr 2014
The Correct Answer and Explanation is:
The correct factor pairs of 91 are as follows: 1 × 91 and 7 × 13. Since 91 is a composite number, it has factors beyond just 1 and itself. The prime factorization of 91 is 7 × 13, meaning it is the product of two prime numbers.
Explanation:
Factor pairs refer to pairs of numbers that, when multiplied together, yield a given number. To find the factor pairs of 91, one must determine which integer values can divide 91 without leaving a remainder. Dividing 91 by various whole numbers reveals that only 1, 7, 13, and 91 meet this criterion.
Prime factorization is the process of breaking down a composite number into its smallest prime components. Since 91 is the product of two prime numbers, its prime factorization is straightforward: 7 × 13.
A number is classified as composite if it has more than two factors. In this case, 91 is divisible by 1, 7, 13, and 91, demonstrating that it is not a prime number. Instead, it belongs to the category of composite numbers.
Incorrect factor pairs such as 2 × 45.5 or 3 × 30.3333 arise from using non-integer values, which do not fulfill the definition of factor pairs. Factor pairs must consist exclusively of whole numbers.
Understanding factorization is fundamental in number theory and algebra, playing a crucial role in simplifying fractions, solving equations, and analyzing numerical relationships. By identifying prime factorizations, mathematicians can determine the least common multiples and greatest common divisors of numbers, contributing to broader applications in various mathematical disciplines
