The Amazing Concepts

Kaprekar number is one of the amazing concepts in Mathematics. The square of a number when divided into parts and none of the parts is equal to 0, and sum of both the parts forms the original number, then that number is a Kaprekar number . Let's understand this concept in detail: Checking a Kaprekar Number Following are the steps to check whether any number is a Kaprekar number or not: Step 1 : Consider any number N (must be greater than 0). Step 2 : Square the number N (N x N). Step 3 : Divide the resultant obtained in Step 2 into two parts (left and right). Possible scenarios that occur when dividing the resultant into two parts: Scenario 1 : If the resultant obtained in Step 2 is a single digit number If the resultant obtained in Step 2 is a single digit number (no matter even or odd), compare it with the number considered in Step 1.  If the number in Step 2 is equal to the number in Step 1, it is a Kaprekar number. But if the number  in Step 2 is not equal to the...

In Mathematics, one of the amazing concepts is the Reverse-Add-Then-Sort (RATS) Sequence. The RATS Sequence is a sequence that is formed by reversing , adding , then sorting the digits. Let's understand this concept in detail: Form the RATS Sequence Step 1 : Consider any number (must be greater than 0). Step 2 : Reverse the number. Step 3 : Add the original number (considered in Step 1) with the number formed by reversing the number (in Step 2). Step 4 : Sort the number obtained in Step 3 in ascending order. The resultant obtained after sorting the number forms the next sequence after n iteration. Examples First Iteration Step 1 : Number 1 . Step 2 : Reversing the number 1  gives the resultant  1 . Step 3 : Adding the original number 1 (considered in Step 1) with the number formed by reversing (in Step 2)  i.e. 1 gives the resultant 2 . Step 4 : Sorting the number obtained in Step 3 in ascending order gives the resultant 2 . Here number 2 forms the next sequence after...

You might have heard the term black hole . A black hole is a region of spacetime where gravity is so strong that even light or electromagnetic waves cannot escape it. In Mathematics, the number 123 is called the black hole number. Let’s understand this amazing concept in detail. The Procedure Step 1 : Consider any number . Step 2 : Count the number of even digits. Step 3 : Count the number of odd digits. Step 4 : Count the number of total digits. Step 5 : Consider the number (" even " " odd " " total ") obtained in the n   iteration. Step 6 : Repeat the steps ( Step 1 to Step 5 ) after every iteration until you get the number (" even " " odd " " total ") as  123 . Note : If you repeat the steps ( Step 1 to Step 5 ) even after getting the number 123, you will obtain the same number i.e. 123 after every iteration. Example First Iteration Step 1 : Number 1234567890 . Step 2 : Number of  even  digits = 5 . Step 3 : Number of...

A triangular number (triangle number) is a number that represents the pattern of dots arranged in a way that they form an equilateral triangle. An equilateral triangle (also known as a regular triangle) is the one in which all the three sides are of equal length. A triangular number is denoted by Tn that represents the number of dots. Mathematical Formula Below is the mathematical formula for a triangular number: where n is a positive number such as 1, 2, 3, 4, 5, ..... , n. Triangular Number Sequence Below is the triangular number sequence: [1, 3, 6, 10, 15, 21, 28, 36, ..... ] Example For n = 1 Putting this value of n in the above mathematical formula: T1 = 1(1 + 1)/2 T1 = 1(2)/2 T1 = 2/2 T1 = 1 For n = 2 Putting this value of n in the above mathematical formula: T2 = 2(2 + 1)/2 T2 = 2(3)/2 T2 = 6/2 T2 = 3 For n = 3 Putting this value of n in the above mathematical formula: T3 = 3(3 + 1)/2 T3 = 3(4)/2 T3 = 12/2 T3 = 6 For n = 4 Putting this value of n in the above mathematical formu...

One of the amazing concepts associated with the numbers is multiplication with three and adding the resultant digits. As per this amazing concept, if any number is multiplied with three and the resultant digits are added all together, then the new resultant digits are divisible by three. The Concept Step 1: Take any number. Step 2: Multiply the number (taken in Step 1) with three. Step 3: Add the resultant digits (obtained in Step 2) all together. Step 4: The new resultant formed in Step 3 is divisible by three. For Example Number 15 Multiply the number with three: 15 x 3 => 45. Add the resultant digits: 4 + 5 => 9. The new resultant is divisible by three: 9 / 3 => 3. Number 25 Multiply the number with three: 25 x 3 => 75. Add the resultant digits: 7 + 5 => 12. The new resultant is divisible by three: 12 / 3 => 4. Number 99 Multiply the number with three: 99 x 3 => 297. Add the resultant digits: 2 + 9 + 7 => 18. The new resu...

Pronic number, also known as Oblong number, Heteromecic number, or Rectangular number, is a positive integer n which is the product of two consecutive integers. Pronic Number Formula Pronic number formula is given below: n (n + 1) Pronic Number Sequence 0, 2, 6, 12, 20, 30, 42, ….., n. For Example Integer : 56 For integer 56, the value of first consecutive integer = 7. Putting this value of first consecutive integer in Pronic number formula: 7 (7 + 1) => 7 x 8 => 56. Integer : 72 For integer 72, the value of first consecutive integer = 8. Putting this value of first consecutive integer in Pronic number formula: 8 (8 + 1) => 8 x 9 => 72. Integer : 110 For integer 110, the value of first consecutive integer = 10. Putting this value of first consecutive integer in Pronic number formula: 10 (10 + 1) => 10 x 11 => 110. Integer : 156 For integer 156, the value of first consecutive integer = 12. Putting this value of first consecu...

In number theory, a Practical number or Panarithmic number is a positive integer n that can represent all smaller numbers m (m < n) as the sums of distinct divisors of n. In other words, any positive integer n having the property that all smaller integers can be represented as the sums of distinct divisors of integer n is referred to as a Practical number or Panarithmic number. The Procedure Step 1:  Consider a positive integer n. Step 2:  Find out the distinct divisors of n. Step 3:  Check whether all numbers smaller than n can be represented as the sums of distinct divisors of n. Step 4:  If all numbers smaller than n can be represented as the sums of distinct divisors of n, then n is a Practical number or Panarithmic number, else not. Practical Number Sequence 1, 2, 4, 6, 8, 12, 16, 18, 20, ….., n. For Example Integer: 24 Distinct divisors of 24: 1, 2, 3, 4, 6, 8, 12. All smaller numbers such as: 5 => 2 + 3 7 => 3 + 4 9 =>...