Olympiad Test: Playing With Numbers - Class 6 MCQ

Numbers which have more than two factors are called composite numbers.

Numbers which have only two factors (1 and itself) are called prime numbers.

• 1: The number 1 is neither prime nor composite. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. Since 1 only has one positive divisor (itself), it does not meet the definition of a prime number. Similarly, a composite number is a positive integer greater than 1 that can be formed by multiplying two smaller positive integers. Since 1 does not meet this criteria either, it is considered neither prime nor composite.

The prime factorization of 36 is: 2 x 2 x 3 x 3

The prime factorization of 72 is: 2 x 2 x 2 x 3 x 3

Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get LCM = 2 x 2 x 2 x 3 x 3 = 72 

• Step 1: Find the prime factors of each number




• 17 = 17 (prime number)


• 5 = 5 (prime number)




• Step 2: Identify the common and uncommon prime factors




• Common prime factors: None


• Uncommon prime factors: 17, 5




• Step 3: Multiply all the prime factors to get the L.C.M.




• L.C.M. = 17 x 5 = 85

No factor except 1 is common to them.

The first few twin prime pairs are: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107, 109), (137, 139), … ... Five is the only prime in two distinct pairs.

H.C.F. of two co-prime numbers is 1.

Of the given options 973572 is an even number.

∴ H.C.F. of 120 & 144 =24

When two factors are multiplied we get a product.

• Factors: A factor of a number divides that number exactly without leaving a remainder.


• Multiples: A multiple of a number is the result of multiplying that number by an integer.

• Every number is considered a factor and a multiple of itself because:
  
  
  
  • A number is always divisible by itself, making it a factor.
  
  
  • The product of a number and 1 is the number itself, making it a multiple.
  
  
  
  


• For example, the number 5:
  
  
  
  • Factors of 5 are 1 and 5 (1 x 5 = 5).
  
  
  • Multiples of 5 are 5, 10, 15, 20, and so on.
  
  
  
  

• Therefore, every number is both a factor and a multiple of itself due to the nature of division and multiplication.


• This relationship holds true for all integers, making it a fundamental property of numbers.

• Definition: Even numbers are integers that are divisible by 2 without leaving a remainder.


• Examples: 2, 4, 6, 8, 10, etc.


• Properties:
  
  
  
  • Even numbers always end in 0, 2, 4, 6, or 8.
  
  
  • When you add or subtract two even numbers, the result is always an even number.
  
  
  • Even numbers are opposite to odd numbers in the number line.
  
  
  
  

• H.C.F. (Highest Common Factor) of two numbers is the greatest number that divides both of them without leaving a remainder.


• L.C.M. (Least Common Multiple) of two numbers is the smallest number that is a multiple of both numbers.


• Let the two numbers be a and b, and their H.C.F. be x and L.C.M. be y.


• According to the property, a * b = x * y.


• Therefore, x = (a * b) / y.


• So, the H.C.F. of the two numbers is equal to the product of the numbers divided by their L.C.M.


• Hence, the correct answer is Option A: Product of the numbers divided by their L.C.M.

1 is a factor of every number.

1 is not a prime number so these are all possible prime numbers between 1 to 50

“2,3,5,7,11,13,17,19,23,29,31,37,41,43,47” which are 15 in number

2,3,5,7,11,13,17,19,23,29,31,37,41,43,47

A = 11 and
B = 17
17-11 = 6

53 and 59 are the prime number between 50 and 60

A: 2 × 2 × 7 = 28

B: 2 × 2 × 5 = 20

C: 2 × 2 × 5 × 7 = 140

D: 2 × 2 × 5 × 7 × 3 = 420

Even numbers are 2,4,6,8,10 and so on.

In between these even numbers, we have odd numbers 3,5,7,9..

Hence, successor of even number, is an odd number.