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Numbers

Types of Numbers

Hello students, welcome to my new series of Aptitude, in this blog we are going to learn about numbers. Numbers is the very basic thing in Aptitude learning. Numbers starts from Zero "0". Zero was firstly invented by Aryabhata. Lets learn more about numbers.

Types of numbers..

  1. Integers:

    2. All the numbers whose fractional part is zero are known as Integers. For e.g. -6, -4, 0, 1, 99, 1000, etc.

  2. Natural Numbers:

    3. All the numbers whose fractional part is zero and also they are greater than zero are termed as natural numbers. For e.g. 1, 2, 3, 4,..., upto n.

  3. Whole Numbers:

    4. All the numbers whose fractional part is zero, including zero are termed as natural numbers. For e.g. 0, 1, 2, 3, 4,..., upto n.

  4. Prime Numbers:

    5. All the numbers having only two factors, the number itself and 1, are termed as prime numbers. For e.g. 2, 3, 19, 7, etc. 1 is not prime, nor composite number. 2 is the smallest even prime number. There are total 25 prime numbers upto 100. They are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

  5. Composite Numbers:

    6. All the numbers excluding prime numbers are known as Composite numbers. For e.g. 60, 4, 49, etc.

  6. Co-prime Numbers:

    7. If the Highest Common Factor of any two numbers is 1 then they are termed as co-primes of each other. To find the co-prime of a number, find the factors of the number first. Then, choose any number and find the factors of the chosen number. All the numbers which do not have any common factor other than 1 will be the co-prime of the given number. If ‘a’ and ‘b’ are co-primes and we have a number ‘n’ that is divisible by both ‘a’ and ‘b’, ‘n’ will be divisible by a x b. For e.g, 18 and 35 are co-prime numbers. The factors of 18 are 1, 2, 3, 6, 9, and 18 while the factors of 35 are 1, 5, 7, and 35. Since the HCF is 1, they are coprime.

Divisibility tests..

  • Divisible by 2:
    • If the last digit of any number is of 0, 2, 4, 6, 8 then the number is said to be divisible by 2.
  • Divisible by 3:
    • If the sum of all the digits in number is divisible by 3 then the number is said to be divisible by 3. For e.g, 18 is divisible by 3 because 1 + 8 = 9 and 9 is divisible by 3.
  • Divisible by 4:
    • If the two last digits of any number are divisible by 4 then the number is said to be divisible bt 4. For e.g, 132 is divisible by 4 because 32 is divisible by 4.
  • Divisible by 5:
    • If the last digit of any number is of 0 & 5 then the number is said to be divisible by 5.
  • Divisible by 7:
    • A number is divisible by 7 if repeatedly doing following steps until a single digit left leaves the single digit as 0 or 7. For e.g, given number is 196. After removing last digit, we get 19. After subtracting 12 (double of removed digit), we get 7. Since the last left digit is 7, number is multiple of 7.
  • Divisible by 8:
    • A number is divisible by 8 if the last three digits are divisible by 8. For e.g, 1234.
  • Divisible by 9:
    • If the sum of all the digits in number is divisible by 9 then the number is said to be divisible by 9. For e.g, 18 is divisible by 9 because 1 + 8 = 9 and 9 is divisible by 9.
  • Divisible by 11:
    • A number is divisible by 11 if the difference between the sum of numbers at even positions and odd positions is either 0 or a multiple of 11. For e.g, 121.

Division Theorem

According to division theorem,

Dividend = Remainder + (Divisor x Quotient).

Practice Questions..

  1. When a number is successively divided by 2, 3, 7, we get 1, 2, 3 as the remainder respectively. What is the smallest such number ?
  2. Which digits should come in place of * and # such that the number 12386*# is divisible by both 8 and 5 ?
  3. More Problems

In closing...

In this blog we learnt about numbers and types of numbers. There are total 10 divisibility tests. I hope you understand this if any query free to mail me at nehalijaiswal1806@gmail.com

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