Composite Numbers are natural numbers greater than 2 that have more than 2 factors.
- Composite numbers are divisible by more than 2 numbers. For example, 4 is divisible by 1, 2 and 4 and 6 is divisible by 1, 2, 3 and 6.
- Every composite number can be uniquely represented as product of prime factors. This is called fundamental theorem of numbers
- Each composite number has at least two prime numbers as its own factors.
- Of all composite numbers, 4 is the smallest and there are infinite number of composite numbers
- Perfect Squares are the only numbers that have odd number of distinct divisors. For example, 9 has divisors as 1, 3 and 9. 4 has divisors as 1, 2 and 4. For all other numbers, divisors appear in pair, so the total number of divisors is always even for other numbers.
- If n is a composite number, then 2n – 1 is always composite. However, if n is prime, then 2n – 1 may or may not be prime.
- Every even number (except 2) is composite.
- 0 and 1 are neither composite nor prime.
- For any composite number, the number of divisors can be calculated using its prime factorization. If a number nn has a prime factorization n = p1e1 × p2e2 x .... x pkek , then the total number of divisors is (e1 + 1)(e2 + 1) … (ek + 1). For example, 12 = 22×31 and the number of divisors is (2+1)(1+1) = 6. We can verify this by writing all divisors of 12 : 1, 2, 3, 4, 6 and 12
- Composite numbers are important in Euler’s totient function, which counts the number of integers less than or equal to n that are https://www.geeksforgeeks.org/maths/co-prime-numbers/relatively prome or co-prime to n. For composite numbers, this value is lower than for primes because they have more divisors. For example, phi(12) = 4, since only 1, 5, 7, and 11 are relatively prime to 12.
Please refer Real Life Applications of Composite Numbers for more interesting things about composite numbers.