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
Monday, January 18, 2016
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
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
Sunday, January 17, 2016
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
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
Mathematically 47
Forty Seven (47)
1. It is a prime number.
2. It is a Lucas number. The Lucas series goes like – 1, 3, 4, 7, 11, 18, 29, 47—
3. It is the first of three consecutive primes (47, 53, 59) that are spaced an equal distance apart. The first such set is (3, 5, 7) and next set is (151, 157, 163)
4. It is the largest number of cubes that cannot tile a cube.
5. The combination of 2 makes an interesting pattern.
47 + 2 = 49 and 49 x 2 = 94
497 + 2 = 499 and 497 x 2 = 994
4997 + 2 = 4999 and 4997 x 2 =9994
49997 + 2 = 49999 and 49997 x 2 = 99994
--------so on
the above pattern shows the same digits in reverse order in two operations.
6. It is the difference of squares of two consecutive numbers.
47 = 24^2 – 23^2
7. There are 47 occurrences of 47 in the first thousand prime numbers.
8. The atomic number of Silver is 47.
9. It is a carol number. A carol number is an integer of the form of 4n – 2n+1 – 1. The first few number are – 1, 7, 47, 223--- This was discovered by Cletus Emmanuel who named it after his friend Carol G Kimon.
Dr Rajesh Kumar Thakur
1. It is a prime number.
2. It is a Lucas number. The Lucas series goes like – 1, 3, 4, 7, 11, 18, 29, 47—
3. It is the first of three consecutive primes (47, 53, 59) that are spaced an equal distance apart. The first such set is (3, 5, 7) and next set is (151, 157, 163)
4. It is the largest number of cubes that cannot tile a cube.
5. The combination of 2 makes an interesting pattern.
47 + 2 = 49 and 49 x 2 = 94
497 + 2 = 499 and 497 x 2 = 994
4997 + 2 = 4999 and 4997 x 2 =9994
49997 + 2 = 49999 and 49997 x 2 = 99994
--------so on
the above pattern shows the same digits in reverse order in two operations.
6. It is the difference of squares of two consecutive numbers.
47 = 24^2 – 23^2
7. There are 47 occurrences of 47 in the first thousand prime numbers.
8. The atomic number of Silver is 47.
9. It is a carol number. A carol number is an integer of the form of 4n – 2n+1 – 1. The first few number are – 1, 7, 47, 223--- This was discovered by Cletus Emmanuel who named it after his friend Carol G Kimon.
Dr Rajesh Kumar Thakur
Mathematically 46
Forty six (46)
1. It is the product of two primes.
46 = 2 x 23
2. It is a centered Triangular number.
3. It is a nonagonal number.
4. It is a centered 15 gonal number.
5. It can be partitioned in 89134 ways.
6. It is the maximal number of regions into which 9 lines divide a plane.
7. The atomic number of Palladium is 46.
8. The number of chromosomes in every cell of human body is 46. 23 of them are inherited from mother and 23 from father.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
1. It is the product of two primes.
46 = 2 x 23
2. It is a centered Triangular number.
3. It is a nonagonal number.
4. It is a centered 15 gonal number.
5. It can be partitioned in 89134 ways.
6. It is the maximal number of regions into which 9 lines divide a plane.
7. The atomic number of Palladium is 46.
8. The number of chromosomes in every cell of human body is 46. 23 of them are inherited from mother and 23 from father.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
Mathematically 45
Forty Five (45)
1. It is a Kaprekar number. A number n is called Kaprekar number if n^2 = xy and x + y = n.
45^2 = 2025 and 20 + 25 = 45
2. It is a triangular number.
3. It is the sum of first nine natural numbers. The formula to sum the n natural number is given by – n (n+1)/2. 1 + 2 + 3+ 4 + 5 + 6+ 7 + 8 + 9 = 45
4. It is the sixth positive integer with a prime factorization in the form of p2q, with p and q are primes.
45 = 3^2 x 5
5. The atomic number of Rhodium is 45.
6. It is the 5th hexagonal number that can be obtained using the formula – n(2n – 1). The hexagonal numbers are – 1, 6, 15, 28, 45---
7. It is a name of card game played between two players as two teams. The winner is the first to gain 45points.
8. It can be partitioned in 75175 ways.
9. It is a 16- gonal number.
10. Here is a mystic rose pattern that contains 45 lines. It is drawn by placing 10 marks around a circle and joining them.
Dr Rajesh Kumar Thakur
1. It is a Kaprekar number. A number n is called Kaprekar number if n^2 = xy and x + y = n.
45^2 = 2025 and 20 + 25 = 45
2. It is a triangular number.
3. It is the sum of first nine natural numbers. The formula to sum the n natural number is given by – n (n+1)/2. 1 + 2 + 3+ 4 + 5 + 6+ 7 + 8 + 9 = 45
4. It is the sixth positive integer with a prime factorization in the form of p2q, with p and q are primes.
45 = 3^2 x 5
5. The atomic number of Rhodium is 45.
6. It is the 5th hexagonal number that can be obtained using the formula – n(2n – 1). The hexagonal numbers are – 1, 6, 15, 28, 45---
7. It is a name of card game played between two players as two teams. The winner is the first to gain 45points.
8. It can be partitioned in 75175 ways.
9. It is a 16- gonal number.
10. Here is a mystic rose pattern that contains 45 lines. It is drawn by placing 10 marks around a circle and joining them.
Dr Rajesh Kumar Thakur
Mathematically 44
Forty four (44)
1. It is the sum of 8 consecutive numbers.
2 + 3 + 4 +5 + 6 + 7 + 8 = 44
2. It is a palindromic number of two digits.
3. It is a Tribonacci number. The Tribonacci numbers are somewhat like Fibonacci numbers with a difference that here the next number is the sum of preceding terms and it starts with 0.
The first few Tribonacci numbers are—0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81—
4. It is an octahedral number. It is a figurative number that represents the number of spheres in an octahedron formed from closed packed spheres. The first few octahedral numbers are--- 1, 6, 19, 44, 85, ---. The nth octahedral number is given by --
5. The atomic number of Ruthenium is 44.
6. It can be partitioned into 63261 ways.
7. Along with number 45, it is the first pair of consecutive numbers with 6 divisors. The sequence of such pairs are- (75, 76), (98, 99), (116,117), (147,148)…
Read More about Numbers in my book - THE POWER OF NUMBERS Published by PRABHAT PRAKASHAN
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Dr Rajesh Kumar Thakur
1. It is the sum of 8 consecutive numbers.
2 + 3 + 4 +5 + 6 + 7 + 8 = 44
2. It is a palindromic number of two digits.
3. It is a Tribonacci number. The Tribonacci numbers are somewhat like Fibonacci numbers with a difference that here the next number is the sum of preceding terms and it starts with 0.
The first few Tribonacci numbers are—0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81—
4. It is an octahedral number. It is a figurative number that represents the number of spheres in an octahedron formed from closed packed spheres. The first few octahedral numbers are--- 1, 6, 19, 44, 85, ---. The nth octahedral number is given by --
5. The atomic number of Ruthenium is 44.
6. It can be partitioned into 63261 ways.
Read More about Numbers in my book - THE POWER OF NUMBERS Published by PRABHAT PRAKASHAN
you can buy this book from FLIPKART, AMAZON, GOOGLEBOOK, SNAPDEAL etc
Dr Rajesh Kumar Thakur
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