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Introduction to Numbers

Express 15 co...

Question

Express 15 composite number as the sum of two prime numbers

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Solution

Dear student, 15 composite number can be expressed as sum of 13 and 2, and both are a prime number.

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as sum of two prime numbers.

State true (T) of false (F):

$(i)$ The sum of primes cannot be a prime.

$(i i)$ The product of primes cannot be a prime.

$(i i i)$ An even number is composite.

$(i v)$ Two consecutive numbers cannot be both primes.

$(v)$ Odd numbers cannot be composite.

$(v i)$ Odd numbers cannot be written as sum of primes.

$(v i i)$ A number and its successor are always co-primes.

Q. Consider the statements regarding prime factorization:

Statement I: The factors in prime factorization of a number are prime numbers.

Statement II: The numbers, having composite numbers as factors, cannot be expressed as prime factorization.

Q. Every composite number can be expressed (factorized) as a product of primes.

Q. If composite number is a product of prime numbers but 15 is a composite number 15=15*1 but if we factorised this then it is not a product of prime numbers.

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