Mathematically 54

Fifty Four (54)
1. It is an abundant number.

2. It is the smallest number that can be written as the sum of 3 squares in 3 different ways.
54 = 7^2 + 1^2 + 2^2 = 6^2 + 3^2 + 3^2 = 5^2 + 5^2 + 2^2

3. It is the sum of first 9 natural numbers starting from 2.
2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 54

4. There are 54 coloured squares on a standard Rubik’s cube. Each of 6 faces has 9 squares. This was invented by Hungarian Sculptor Erno Rubik in 1974.

5. It is a Leyland number. A Leyland number is written in the form of x^y + y^x where x and y are integers greater than 1. The first few Leyland numbers are --- 8, 17, 32, 54, 57---

6. The atomic number of Xenon is 54.

7. It is a Harshad number because it is divisible by the sum of its digits.

8. It is a 19- gonal number.

Dr Rajesh Kumar Thakur

Mathematically 53

Fifty Three (53)


1. It is a Prime number.

2. If there are 53 people in a room it is very likely that at least two of them share the same birthday.

3. It is the only two digit number which on reverse changes into a hexadecimal base.
53 = 3516
4. The sum of all consecutive primes from 7 to 53 is the product of 7 and 53.
7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37+ 41+ 43 + 47 + 53 = 371 = 7 x 53

5. It can be expressed as the sum of squares in two different ways.
53 = 22 + 72 = 12 + 42 + 62

6. The sum of 53 prime numbers is divisible by 53.
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 + 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 + 163 + 173 + 179 + 181 + 191 + 197 + 199 + 211 + 223 + 227 + 229 + 547 = 5830 = 53 x 110

7. The sum of first 53 natural numbers is also divisible by 53.

1 + 2 + 3---- + 53 = 1431 = 53 x 27

8. It is the sum of five consecutive primes starting from 5.
5 + 7 + 11 + 13 + 17 = 53

9. It is the smallest prime which is not the difference between powers of 2 and 3.

10. Atomic number of Iodine is 53.

Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com

Mathematically 52

Fifty Two (52)

1. The number of playing cards is 52. It contains 4 suits (Heart, Diamond, Clubs, and Spades) each of 13 in numbers. The 52 cards have 26 Black and 26 Red Cards. 4 kings, 4 queens, and 4 ace are known as ace cards.

2. It is the sum of two consecutive primes.
52 = 23 + 29

3. A piano has 52 white keys.

4. It is the sum of 6 Fibonacci number starting from the 3rd.
52 = 2 + 3 + 5 + 8 + 13 + 21

5. A year has 52 weeks.

6. It is a 6th Bell number. Bell numbers are named after the mathematician Eric Temple Bell. It is the number of partitions of a set with n members or the number of equivalence relation on it. The first 6 Bell numbers are –
1, 1, 2, 5, 15, 52---

The Bell numbers can be generated by the following table, which works kind of like Pascal's Triangle.

7. It is a decagonal number.

8. It is a 3rd Untouchable number. An untouchable number is a positive integer that can’t be expressed as the sum of all the proper divisors of any positive integer including the untouchable number itself. The first few untouchable numbers are 2, 5, 52, 88---

9. The atomic number of Tellurium is 52.


Dr Rajesh Kumar Thakur

Mathematically 51

Fifty One (51)

1. It is a Pentagonal number as well as Centered Pentagonal number.

2. It is the smallest number which can be written with the digits 1 to 5 as the sum of prime numbers. 51 = 2 + 3 + 5 + 41

3. It is the sum of 6 numbers in an AP with common difference 3.
51 = 1 + 4 + 7 + 10 + 13 + 16

4. It is equal to sum of 6 numbers from 6 to 11.
51 = 6 + 7 + 8 + 9 + 10 + 11

5. It is a 18- gonal number.

6. It is the product of two primes.
51 = 3 x 17

7. It is a 6th Motzkin number. For a given number n, Motzkin number is the number of different ways of drawing chords on a circle between n points. It is named after Theodore Motzkin. The first few Motzin numbers are- 1, 2, 4, 9, 21, 51-----

8. The atomic number of Antimony is 71,

Dr Rajesh Kumar Thakur

Mathematically 50

Fifty (50)

1. It is the smallest number that can be expressed as the sum of two squares in 2 different ways.

50 = 1^2 + 7^2 = 5^2 + 5^2
2. It is equal to the sum of squares of 3 consecutive numbers.
50 = 3^2 + 4^2 + 5^2

3. It can be written as the sum of consecutive prime numbers in two different ways.
50 = 3 + 11 + 13 + 23
= 2 + 5 + 7 + 17 + 19

4. It can be written as the product of complex number and its conjugate.
50 = (7+ i) x ( 7 – i)

5. The atomic number of Tin is 50.

6. It can be written as the sum of digits involving 0 to 9.
50 = 19 + 43/ 2 + 76/5
= 28 + 36/4 + 91/7
= 39 + 21/7 + 64/8

7. It is the sum of squares of first Pythagorean triplet 3 – 4 – 5
50 = 3^2 + 4^2 + 5^2

8. It is a hexagonal pyramid number. It is a pyramidal number formed by adding the first few hexagonal numbers. The first few numbers are – 1, 7, 22, 50..

Dr Rajesh Kumar Thakur

Mathematically 49

Forty Nine(49)
1. It is a square number.
49 = 7 x 7

2. It is the sum of first 7 odd numbers.
1 + 3 + 5 + 7 + 9 + 11 + 13 = 49

3. It is the smallest square whose digits can be separated to make two other squares.
7^2 = 49 = 4 / 9 13^2 =169 = 16 / 9
19^2 = 361 = 36 / 1 35^2 = 1225 = 1 / 225

4. Its cube ends with 49.
49^3 = 117, 649

5. If you put 48 in the middle of number 49 and its successive results, a square number will be formed each time.

4 48 9 = 67^2
44 48 89 = 667^2
444 48 889 = 6667^2

6. The reciprocal of 49 is a repeating decimal with a period of 42.
1⁄49 = 0.0204081632 6530612244 8979591836 7346938775 51

7. The atomic number of Indium is 49.

8. It is a centered octagonal number.

9. The square of 49 = 2401 whose sum 2 + 4 + 0 + 1 =7 is a square root of 49.


Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com

Mathematically 48

Forty Eight (48)

1. It is the smallest number with exactly 10 divisors. Its divisors are- 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

2. It is the smallest even number that can be expressed as a sum of two primes in 5 different ways.
48 = 5 + 43 = 11 + 37 = 7 + 41 = 17+ 31 = 19 + 29

3. It is equal to number of hours in 2 days.

4. The square of 48 can be expressed as the sum of squares of 9 terms of an AP of common difference 3.
48^2 = 2^2 + 5^2 + 8^2 + 11^2+ 14^2 + 17^2 + 20^2 + 23^2 + 26^2

5. It is a Harshad number. Harshad number is divided by the sum of its digits.
48 ÷ 12 (4 + 8) = 4

6. The product of all proper divisors of 48 is equal to 48^4.
48^4 = 1 x 2 x 3 x 4 x 6 x 8 x 12 x 16 x 24 = 5308416

7. The atomic number of Cadmium is 48.

8. It is an abundant number.

9. It is a 17- gonal number.

10. The Rhombicuboctahedron is an Archimedan solids with 48 edges.

Dr Rajesh Kumar Thakur