Define the following terms : (a) Co-prime (b) Twin-prime (c) Perfect numbers
Answers
Step-by-step explanation: Twin prime- Two prime numbers are called twin primes if there is present only one composite number between them. Or we can also say two prime numbers whose difference is two are called twin primes. For example, (3,5) are twin primes, since the difference between the two numbers 5 – 3 = 2. The alternative names, given to twin primes are prime twin or prime pair.
Co prime- Numbers which has no factors except 1 are called co prime numbers.
Perfect numbers-In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. The smallest perfect number is 6, which is equal to the sum of 1,2, and 3. Other perfect numbers are 28, 496, and 8128. It is not known when perfect numbers were first studied and indeed the first studies may go back to the earliest times when numbers first aroused curiosity. It is quite likely, although not certain, that the Egyptians would have come across such numbers naturally given the way their methods of calculation worked
Answer :-
(a) Co-prime:
All pairs of two consecutive numbers
are co-prime numbers. Any two consecutive numbers have 1 as their common factor.
Ex :- 2 and 3, 5 and 7, 11 and 13
(b) Twin-prime:
A twin prime is a prime number that is either 2 less or 2 more than another prime number.
Ex:- either member of the twin prime
pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two.
(c) Perfect numbers: