6. Identify each of the following numbers as prime OR composite.
121 → Composite (b) 833 → Composite
(c) 900 058 812 709 003 → Prime (d) 292 → Composite
(e) 17 → Prime.
(a) 121 → Composite: A composite number is a positive integer that has more than two positive divisors. 121 can be divided by 1, 11, and 121. Since it has more than two divisors, it is composite.
(b) 833 → Composite: A composite number is a positive integer that has more than two positive divisors. 833 can be divided by 1, 7, 119, and 833. Since it has more than two divisors, it is composite.
(c) 900 058 812 709 003 → Prime: A prime number is a positive integer greater than 1 that has no divisors other than 1 and itself. 900 058 812 709 003 cannot be divided by any positive integer other than 1 and itself. Therefore, it is prime.
(d) 292 → Composite: A composite number is a positive integer that has more than two positive divisors. 292 can be divided by 1, 2, 4, 73, and 292. Since it has more than two divisors, it is composite.
To identify whether a number is prime or composite, we need to understand the properties of prime and composite numbers.
Prime Numbers:
A prime number is a number that is greater than 1 and has only two distinct factors - 1 and itself. In other words, a prime number cannot be divided evenly by any other number besides 1 and itself.
Composite Numbers:
A composite number is a number that has more than two distinct factors. In other words, it can be divided evenly by numbers other than 1 and itself.
Now let's apply this knowledge to the given numbers:
(a) 121:
To determine if 121 is prime or composite, we need to find its factors. We can start by checking if it is divisible by any numbers from 2 to the square root of 121. If we find any factors, it would be composite.
121 divided by 11 gives us 11, which means that it has a factor of 11. Therefore, 121 is a composite number.
(b) 833:
Similar to the previous case, we need to find the factors of 833. Dividing it by numbers from 2 to the square root of 833, we can determine if it is prime or composite.
833 divided by 7 gives us 119, which means that it has a factor of 7. Therefore, 833 is a composite number.
(c) 900,058,812,709,003:
To determine if this number is prime or composite, we need to find its factors. However, directly calculating the factors for such a large number is not a practical approach.
Alternatively, we can use the concept of prime factorization. If a number can be expressed as the product of two or more prime numbers, then it is composite. Otherwise, it is prime.
Checking if any numbers divide evenly into 900,058,812,709,003, we find that it cannot be divided evenly by any number other than 1 and itself. Hence, it has no other factors, indicating that it is a prime number.
Therefore, 900,058,812,709,003 is a prime number.
(d) 292:
Similar to the previous cases, let's find the factors of 292 by dividing it by numbers from 2 to the square root of 292.
292 divided by 2 gives us 146, which means that it has a factor of 2. Therefore, 292 is a composite number.
Summary:
(a) 121 → Composite
(b) 833 → Composite
(c) 900,058,812,709,003 → Prime
(d) 292 → Composite