Mathematically 36

Thirty Six (36)


1. It is a triangular number and a square number. It is better known as a square triangular number. It is the smallest number with this property.

2. The total number of sample space of throwing 2 dices is 36.

3. It is the smallest number which is the sum of pairs of distinct odd primes in four ways.
36 = 5 + 31 = 7 + 29 = 13 + 23 = 17 + 19

4. It is the 6th abundant number.

5. It can be partioned into 17977 ways.

6. It can be expressed as the sum of cubes of three consecutive numbers.
36 = 1^3 + 2^3 + 3^3

7. It is the smallest number to have 9 different factors—1, 2, 3, 4, 6, 9, 12,18 and 36.

8. 1 yard = 36 inches.

9. It is the product of squares of first three integers.
36 = 1^2 x 2^2 x 3^2

10. It is the only triangular number other than 1 whose square root is also a triangular number.

11. The interior angle of each tip of a regular pentagram is 36. A pentagram is the shape of a five pointed star drawn with 5 straight strokes.

12. It is the smallest square with the property that n/2 – 1 and n/2 + 1 are both primes.

13. The truncated cube and truncated octahedron both have 36 edges and both are the Archimedean solids.

14. It is the largest 2 digit number divisible by the product of its digits and also by their sum.
36 is divisible by 3 x 6 = 18 and 3+6 = 9

15. The sum of first 36 number is 666- a beast number
1 + 2 + 3 + ---- + 36 = 666

16. The Kiwi's seed divides the circle into 36 equal sectors. (From Pat's Blog - http://pballew.blogspot.in/)

Dr Rajesh Kumar Thakur

35 Mathematically

Dr Rajesh Thakur

34 Mathematically

Thirty Four (34)

1. It is the 9th Fibonacci number. The Fibonacci series goes like--1, 1, 2, 3, 5, 8, 13, 21, 34—

2. All 4 x 4 magic square has a magic constant 34.

8 11 5 10
13 2 16 3
1 14 4 15
12 7 9 6

3. It is the smallest number with the property that it and its neighbours have the same number of divisors. 34 has 4 divisors so as its neighbours 33 and 35.

4. It is a heptagonal number. A heptagonal number is a figurative numbers that represents a heptagon. The nth heptagonal number is given by

5. It can be partioned into 12310 ways.

6. It is the smallest number which can be expressed as the sum of two primes in four distinct ways.

34 = 3 + 31 = 5 + 29 = 11 + 23 = 17 +17

7. The atomic number of Selenium is 34.

Dr Rajesh Thakur

33 Mathematically

Thirty Three (33)
1. It is the smallest odd repdigit that is not a prime number.

2. It is the sum of first four factorials.
33 = 1! + 2! + 3! + 4!

3. It can be partioned in 10143 ways.

4. It is the smallest member of triplets of successive semi primes. A semi prime is a number with only two
factors.

5. It is the largest positive integer that cannot be expressed as a sum of different triangular numbers.

6. It is a palindrome number on base 10 and also on base 2.
(33)10 = (100001)2

7. The atomic number of Arsenic is 33.

8. On Newtonian scale, it is the temperature on which water boils.

9. Any integer greater than 33 can be written as the sum of 5 non- zero squares.

10. It is a 3rd 12-gonal number

11. It is the number of Perfect graphs with 3 vertices.

12. The Sagrada Familia cathedral in Barcelona designed by Antoni Gaudí is a mathematician’s dream .The cathedral also contains a Magic Square — an arrangement of numbers that equal the same amount in every column, row, and diagonal. The magic number in Sagrada Familia’s case is 33, which alludes to multiple religious symbols. For example, Jesus performed 33 recorded miracles, and most Christians believe he was crucified at 33 years old in 33 A.D

Dr Rajesh Thakur

Importance of Number 32

Thirty two (32)

1. In chess there are 32 pieces on the board at the start of the game.

2. It is the third Leyland number. A Leyland number is written in the form of x^y + y^x.
32 = 2^4 + 4^2

3. It is the melting point of ice on the Fahrenheit scale.

4. A football has 32 panels with 12 regular pentagons and 20 regular hexagons. The football shape is called a Truncated Icosahedrons.

5. It can be partioned into 8349 ways.

Read more about any Number in my book
The Power of Numbers
by Prabhat Publication available on Flipkart, Amazon and other websites

Dr Rajesh Kumar Thakur

Mathematically 31

                                                     Thirty One (31)

1. It is a prime number.

2. It is the sum of five powers of 2.

2^0 + 2^1 + 2^2 + 2^3 + 2^4 = 31

3. It is the third Mersenne prime.
2^5 – 1 = 31

4. January, March, May, July, August, October, December have 31 days.

5. Sum of first 31 odd primes is a perfect square.
3 + 5 + 7 + 11 + …. + 83 + 87 + 89 = 31^2

6. It is a Centered Pentagonal number.

7. It is a repdigit in base 5 and base 2.
(111)5 = (11111)2 = 31

8. The numbers 31, 331, 3331, 33331, 333331, 3333331, and 33333331 are all prime but 333333331 is not a prime.

9. It can be partioned into 6842 ways.

10. It is amongst the two known number that can be written in 2 ways as the sum of successive powers starting with 1.
31 = 1 + 5 + 5^2                                               31= 1 + 2 + 2^2 + 2^3 +2^4

11. It is the sum of first two primes raised to themselves.

31 = 2^2 +3 ^3

12. The digit sum of 31st Fibonacci number (1346269) is 31
1 + 3 + 4 + 6 + 2 + 6 + 9 = 31

13. The number obtained by raising the first four prime to themselves comes out to be a prime.
22+33+55+77=826699


14 . It is a Happy Prime. A happy prime is a number that is both happy and prime.
The first happy primes are 7, 13, 19, 23, 31, 79 etc.
A happy number is defined in the following way:-- Start with any number, replace the number
by the sum of the squares of its digits. Repeat the process until you get 1.

15. It is the minimal move required to solve the Tower of Hanoi puzzle with 5 disks.


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Dr Rajesh Thakur
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Mathematically 30

Thirty (30)

1. It is the product of first three prime numbers.
30 = 2 x 3 x 5

2. It is the sum of first fours square number.
30 = 1^2 + 2^2 + 3^2 + 4^2

3. It is a Pyramidal number. A pyramidal number is a figurative number that represents a pyramid with a base and a given number of sides.

4. It is the largest number such that every smaller co prime to it is a prime.

5. Dodecahedron and Icosahedrons both have 30 edges.

Dodecahedron Icosahedron
6. A polygon with 30 sides is called a tricontagon.

7. It is a Harshad number because 30 is divisible by the sum of its digit 3 + 0 = 3.

8. The atomic number of zinc is 30.

9. It is the area of right angle triangle with side 5, 12 and 13. It also has the perimeter 30.

10. It is the 5th abundant number.

11. N^5 – N is divisible by 30.

12. It is a round number. A number (n) is said to be a round number if it has no prime factor greater than square root n.


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Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com