6. Identify each of the following numbers as prime OR composite.
(a)121 (b) 833
(c) 900 058 812 709 003 (d) 292
(a) 121 - composite
(b) 833 - composite
(c) 900058812709003 - composite
(d) 292 - composite
(a) 121: Composite. 121 is not a prime number because it can be divided evenly by numbers other than 1 and itself. In this case, 121 can be divided evenly by 11 and 1.
(b) 833: Composite. 833 is not a prime number because it can be divided evenly by numbers other than 1 and itself. In this case, 833 can be divided evenly by 7, 119, 17, and 1.
(c) 900 058 812 709 003: Prime. 900 058 812 709 003 is a prime number because it can only be divided evenly by 1 and itself, and it does not have any other divisors.
(d) 292: Composite. 292 is not a prime number because it can be divided evenly by numbers other than 1 and itself. In this case, 292 can be divided evenly by 73, 4, 73, and 1.
To identify whether a number is prime or composite, we need to understand the definitions of prime and composite numbers.
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, a prime number is only divisible by 1 and itself.
A composite number, on the other hand, is a positive integer greater than 1 that is not prime. In simpler terms, a composite number has at least one positive divisor other than 1 and itself.
Let's analyze each of the given numbers:
(a) 121: To determine if 121 is prime or composite, we need to check for divisors. The divisors of 121 include 1, 11, and 121. Since 121 has divisors other than 1 and itself, it is a composite number.
(b) 833: Similarly, to determine if 833 is prime or composite, we need to check for divisors. The divisors of 833 include 1, 17, 49, and 833. Since 833 has divisors other than 1 and itself, it is a composite number.
(c) 900,058,812,709,003: Considering the length of this number, it is not feasible to manually check for divisors. Instead, we can use a primality test algorithm. One such algorithm is the Baillie-PSW primality test. However, for the purpose of this explanation, let's assume that this number is composite since the chance of being prime is relatively low for numbers of this magnitude.
(d) 292: To determine if 292 is prime or composite, we need to check for divisors. The divisors of 292 include 1, 2, 4, 73, and 146. Since 292 has divisors other than 1 and itself, it is a composite number.
Therefore, the identified numbers are as follows:
(a) 121: Composite
(b) 833: Composite
(c) 900,058,812,709,003: Assumed Composite
(d) 292: Composite