Playing With Numbers - Free MCQ Practice Test solutions, Class 6 1000+

• 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.”

To determine the sum of two odd numbers and one even number, we can use the properties of odd and even numbers:

• An odd number can be represented as 2m+1 where m is an integer.
• An even number can be represented as 2n where n is an integer.

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.

To determine the maximum number of consecutive numbers less than 100 with no prime numbers between them, we need to identify a sequence of consecutive composite numbers.

The longest sequence of consecutive composite numbers less than 100 is from 90 to 96:

• 90 (composite)
• 91 (composite)
• 92 (composite)
• 93 (composite)
• 94 (composite)
• 95 (composite)
• 96 (composite)

This sequence has 7 consecutive composite numbers, meaning there is no prime number in this range.

So, the correct answer is:

3. 7

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.

• Co-prime numbers are two numbers that have no common factors other than 1.
• For example, 8 and 15 are co-prime because their only common factor is 1.
• This property is important in various mathematical concepts, including fractions and number theory.
• In contrast, odd numbers, prime numbers, and composite numbers can share common factors, which disqualifies them from being co-prime.

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.