Test: Playing With Numbers

• Prime numbers are the positive integers having only two factors, 1 and the integer itself.
• Any number which does not follow this is termed as composite numbers.
• The smallest prime number as defined by modern mathematicians is 2.

• 2 is the only even Prime Number.
• More interesting fact is that 2 is the smallest prime number.
• Many of us has the misconception that 1 is the smallest prime number, but as per standard definition of prime number “A number which has 2 factors 1 and itself is said to be a prime number.”

We know that sum of two odd numbers is always even. Adding one more even number will keep the result an even number.

In mathematics, composite numbers also known as composites in Mathematics are numbers that have more than 2 factors, not like prime numbers that have only one factor, i.e. 1 and the number itself. Composite numbers are all natural numbers that are not prime numbers since they can be divided by more than two numbers.

Therefore

• The smallest composite number is 4. The smallest composite number of 2 digits is 10.
• 4 is a composite number because there are 2 variables. One is 1 × 4 = 4 and the other is 2 × 2= 4.

For 7 consecutive composite numbers, there should be 2 prime numbers with atleast a difference of 8. And that's possible only between 89 and 97.
So the numbers are 90,91,92,93,94,95,96.

A number is divisible by 6 if the number is divisible by both 2 and 3.

A number is divisible by 3 if the sum of the digits of the number is divisible by 3(1 + 2 + 3 = 6).

Whole numbers are divisible by 4 if the number formed by the last two individual digits is evenly divisible by 4.

For example, the number formed by the last two digits of the number 3628 is 28, which is evenly divisible by 4 so the number 3628 is evenly divisible by 4.

The two numbers which have only 1 as their common factor are called co-primes.

A number is divisible by 10, if its ones digit is 0.
A number is divisible by 5, if its ones digit is 0 or 5.