Write the factors of 91 and find out whether it is a prime or composite number.
The correct answer and explanation is:
Answer:
The factors of 91 are 1, 7, 13, and 91.
Therefore, 91 is a composite number.
Explanation:
To determine whether 91 is a prime or composite number, start by identifying its factors. A factor is any whole number that divides another number without leaving a remainder. Every number has at least two factors: 1 and itself. If those are the only two factors, the number is prime. If the number has additional factors, it is composite.
Begin by checking for divisibility:
- 91 is not even, so it is not divisible by 2.
- The sum of its digits is 9 + 1 = 10, which is not divisible by 3, so it is not divisible by 3.
- It does not end in 0 or 5, so it is not divisible by 5.
- Dividing 91 by 7, the result is 13, and 13 is a whole number. That shows both 7 and 13 divide 91 exactly.
This means 91 has four distinct factors: 1, 7, 13, and 91.
Since it has more than two factors, 91 is not a prime number. It is classified as a composite number, which means it is made by multiplying smaller natural numbers.
In fact, 91 = 7 × 13, both of which are prime numbers. When two prime numbers are multiplied together, the result is always composite, unless one of them is 1, which is neither prime nor composite.
Understanding whether a number is prime or composite is important in number theory, especially in fields like cryptography, algebra, and computer science. Knowing the factors of a number helps in simplifying fractions, finding least common multiples, and solving equations. Therefore, recognizing that 91 is composite helps improve number sense and mathematical reasoning.