Is 81 prime or composite?
Understand the Problem
The question is asking whether the number 81 is classified as a prime number or a composite number. A prime number is only divisible by 1 and itself, while a composite number has divisors other than 1 and itself.
Answer
81 is a composite number.
Answer for screen readers
The number 81 is a composite number.
Steps to Solve
- Defining Prime and Composite Numbers
Recall the definitions: a prime number has exactly two distinct positive divisors, which are 1 and the number itself, while a composite number has more than two divisors.
- Finding Divisors of 81
To determine the classification of 81, we will find its divisors.
Starting with 1 and 81:
- 1 is a divisor of every number.
- Now we check for other divisors by dividing 81 by integers up to $\sqrt{81}$.
- Identifying Divisors through Division
We can check the numbers:
- $81 \div 1 = 81$
- $81 \div 3 = 27$
- $81 \div 9 = 9$
So the divisors of 81 are: 1, 3, 9, 27, and 81.
- Counting the Divisors
We find that the total number of distinct divisors of 81 is 5 (1, 3, 9, 27, 81).
- Classifying the Number
Since 81 has more than two distinct positive divisors, we conclude that it is a composite number.
The number 81 is a composite number.
More Information
In math, composite numbers like 81 can be expressed as products of prime factors. The prime factorization of 81 is $3^4$ (since $3 \times 3 \times 3 \times 3 = 81$). This indicates how many times the prime number 3 is multiplied to get 81.
Tips
A common mistake is confusing prime and composite definitions. Some may think a composite number is any number greater than 1, but a prime must have exactly two divisors.
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