Question

Why is 1 neither prime nor composite?

Is 22/7(3.14........)a rational number?according to p/q it is a rational but it is non terminating repeting decimal so it is irrational.so it is rational or irrational?

Answer 1

Prime numbers are the ones that can be divided by only two positive integers namely itself and 1 i.e prime numbers have only two factors.
for example: 13 can be divided only by 1 and 13.
Since 13 has only two factors it is a prime number.

Composite numbers are the ones that can be divided by more than two positive integers i.e. composite numbers have more than two factors.
for example:8 can be divided by 1, 2, 4, and 8.
Since 8 has more than two factors it is composite.

But, 1 can be divided by just one positive integer which is 1 itself i.e. 1 has only one factor.
So 1 does not fit in the definition of either prime or composite number.
Hence 1 is neither prime nor composite.

Irrational numbers can't be represented as a fraction with integers as the numerator and denominator. 22/7 is a fraction with integers as it's numerator and denominator. Therefore, 22/7 is not irrational,it is a rational number.

22/7 is often used as an approximation for ππ. However, 22/7 does not equal π.
22/7≈3.14285714
while π≈3.1415926536