Mathematically 38

Thirty Eight (38)

1. The only possible magic hexagon has the magical constant as 38. The following magic hexagon has the digits from 1 to 19.

2. It is the largest known even number which can be represented as the sum of two distinct primes in one and only one way.

38 = 31 + 7

3. It is the sum of squares of first three primes.

38 = 2^2 + 3^2 + 5^2

4. 38th digit of pi (excluding decimal) is a Prime number
 31415926535897932384626433832795028841 

5. It is the largest even number which cannot be written as the sum of two odd composite numbers.

6.

5. The atomic number of Strontium is 38.

6. It is the product of two prime factors.
38 = 2 x 19

Dr Rajesh Kumar Thakur

Mathematically 37

Thirty Seven


1. It is the fourth Hexagonal number, because it can be arranged in a pattern of nested hexagon.

2. It is a prime number.

3. Normal body temperature of a healthy man is 37 degree C

4. If you multiply 37 with the multiple of 3 you will get an astonishing result.
37 x 3 = 111
37 x 6 = 222
37 x 9 = 333
37 x 12 = 444 etc.

5. Take any 6 digit number in which the first three digits are consecutively increasing and last three digits are consecutively decreasing, the number will be divisible by 37.
123987 is divisible by 37

6. It is the only two digit number which, when multiplied by 2 and subtracted by 1 gives the number in reverse order.
2 x 37 – 1 = 73 is reverse of 37

7. The atomic number of Rubidium is 37

8. 37 and 38 are the first pair of consecutive positive integers not divisible by any of their digits.

9. The reciprocal of 37 has three periods.
1/37 = 0.027 027 027 …
It is the only prime that has three digit periods after decimal expansion.

10. It is a centered 12- gonal number.

11. It is a maximal number of regions into which 8 lines divide a plane.

12. It can be partioned in 21687 ways.

Dr Rajesh Kumar Thakur

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