In mathematics, a prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. A composite number is a natural number that can be formed by multiplying two smaller natural numbers. Prime numbers have many interesting properties. For example, the sum of any two prime numbers is also a prime number. This is not true for composite numbers. The product of any two composite numbers is also a composite number.
To check if a number is prime or composite, you can use the following algorithm:
- Iterate through a range of numbers from 2 to the square root of the number you are checking.
- For each number in the range, check if the number you are checking is divisible by it.
- If the number is divisible by any number in the range, it is a composite number.
- If the number is not divisible by any number in the range, it is a prime number.Can a number transform as prime or composite ?
No, a number cannot change from being prime to composite or vice versa. A prime number is a positive integer greater than 1 that is divisible by only 1 and itself, and a composite number is a positive integer greater than 1 that is divisible by at least one positive integer other than 1 and itself. Once a number is determined to be either prime or composite, it will always be that way.
Do Prime numbers divide Prime number ?
Prime numbers can divide other numbers, including other prime numbers. However, when a prime number divides another prime number, the result is always a composite number.
For example, if we take the prime number 3 and divide it by another prime number, say 5, we get the result of 0.75 (3/5) which is a decimal number, not an integer. Therefore 5 is not a divisor of 3.
In summary, prime numbers can divide other numbers, including other prime numbers, but the result will always be a composite number (unless the divisor is 1).
Do Composite numbers divide Composite number ?
Yes, composite numbers can divide other composite numbers.
When a composite number divides another composite number, the result can be either an integer or a decimal, depending on whether the division is exact or not.
For example, consider the composite numbers 12 and 15. 12 is divisible by 3 and 4, while 15 is divisible by 3 and 5. When we divide 12 by 15, the result is 0.8 which is a decimal number, and 12 is not divisible by 15.
On the other hand, consider the composite numbers 12 and 6. 12 is divisible by 3 and 4, while 6 is divisible by 2 and 3. When we divide 12 by 6, the result is 2 which is an integer number, and 12 is divisible by 6.
In summary, composite numbers can divide other composite numbers, and the result can be either an integer (in case of exact division) or a decimal (in case of non-exact division).
