Determine whether each of the following numbers is prime or composite
(a)219
(b)791
(c) 1001
Prime means the number cannot be divided by any other numbers besides itself and 1. Composite is when the number can be divided. Try using a calculator to see if those numbers are divisible, or use divisibility tricks if you know them.
To determine whether a number is prime or composite, you need to check if it is divisible by any other number except 1 and itself. Let's go through each number:
(a) 219:
To check if 219 is prime or composite, we need to see if it is divisible by any number from 2 to 218. If 219 is divisible by any number in this range, then it is a composite number; otherwise, it is a prime number.
To check if 219 is divisible by any number, you can start dividing it by numbers starting from 2 and go up to the square root of 219. If at any point you find a divisor, then 219 is a composite number.
In this case, the square root of 219 is approximately 14.798.
Dividing 219 by numbers from 2 to 14, we find that 219 is divisible by 3. Therefore, 219 is a composite number.
(b) 791:
Similar to the previous case, we need to check if 791 is divisible by any number from 2 to 790. If it is divisible by any number, it is a composite number; otherwise, it is a prime number.
The square root of 791 is approximately 28.111.
Dividing 791 by numbers from 2 to 28, we do not find any divisor. Therefore, 791 is a prime number.
(c) 1001:
Again, we need to check if 1001 is divisible by any number from 2 to 1000. If so, it is a composite number; otherwise, it is a prime number.
The square root of 1001 is approximately 31.638.
Dividing 1001 by numbers from 2 to 31, we find that it is divisible by 7. Therefore, 1001 is a composite number.
To summarize:
(a) 219 is a composite number.
(b) 791 is a prime number.
(c) 1001 is a composite number.