CLICK HERE TO CHECK CLASS XII MATHS NCERT BOOK SOLUTIONS.

Special properties of number 30 (Today’s Date)

1. 30 is the sum of the first four squares, which makes it a square pyramidal number.
2. The icosahedron and the dodecahedron are Platonic solids with 30 edges. 
3. 30 is a Harshad number ( an integer that is divisible by the sum of its digits)
4. The atomic number of zinc is 30
5. The minimum age for United States senators.
6. February 30 is usually used as a sarcastic date for referring to something that will never happen or will never be done.

Special properties of number 29 (Today’s Date)

1. None of the first 29 natural numbers have more than two different prime factors. This is the longest such consecutive sequence.
2. 29 is the sum of three consecutive squares i.e. 29 =  2^2 + 3^2 + 4^2
3. The number of days February has in leap years.
4. The atomic number of copper
5. Saturn requires over 29 years to orbit the Sun.
6. Number of states in india

Special properties of number 28 (Today’s Date)

1. 28 is a triangular number since it is the sum of the first seven counting numbers: 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28.
2. 28 is also a perfect number since the sum of its aliquot divisors (factors that are less than the number itself) is also 28. The aliquot factors of 28 are 1, 2, 4, 7, and 14, and 1 + 2 + 4 + 7 + 14 = 28. The next smallest perfect number is 6, and the next highest perfect number is 496.
3. 28 is an example of a happy number. When you square the digits, add them, and repeat this process on the resulting number, you eventually end up with 1:
2^2 + 8^2 = 68
6^2 + 8^2 = 100
1^2 + 0^2 + 0^2 = 1
4. The sum of the first five prime numbers is 2 + 3 + 5 + 7 + 11 = 28.
5. 28 is a hexagonal number, but not a centered hexagonal number. Every hexagonal number is also a triangular number, but not every triangular number is a hexagonal number.
6. A polygon with 28 sides is called an icosikaioctagon.
7. Between the years 2000 and 2099, the calendar repeats every 28 years. It also cycles every 28 years between 2101 and 2199. 

Special properties of number 27 (Today’s Date)

1. Twenty-seven is a perfect cube = 3^3.
2. In base 10, it is the first composite number not evenly divisible by any of its digits.
3. 27 is the only positive integer that is 3 times the sum of its digits.
4. 27 is a Harshad number (a number divisible by sum of its digits).
5. 27 is the smallest 2-digit number in which the sum of digits is equal to the sum of prime factors, e.g.: 27 = 3 x 3 x 3 and 2 + 7 = 3 + 3 + 3 = 9
6. 23 is the largest integer which is the sum of the digits of its cube:
27^3 = 19,683 and 27 = 1 + 9 + 6 + 8 + 3
7. 27 is the number of "cubies" in a Rubik's cube.
8. The numbers of atoms in the body of an average male (about 80 kg) is about 10^27.
9. The Chemical Element Cobalt has an atomic number of 27.
10. The primitive Greek alphabet had 27 letters.
11. There are 27 signs of the zodiac in Indian astrology

Special properties of number 26 (Today’s Date)

1. 26 is the only number sandwiched between a square (5^2) and a cube (3^3).
2. There are 26 letters in the English alphabet.
3. In base ten, 26 is the smallest number that is not a palindrome to have a square (26^2 = 676) that is a palindrome.
4. In a normal deck of cards, there are 26 red cards and 26 black cards.
5. The Chemical Element Iron has an atomic number of 26.
6. 26 is the number of bones in the normal human Foot and Ankle.
7. There are 26 weeks in half a year.

Special properties of number 25 (Today’s Date)

1. It is a square number, being 5^2 = 5 × 5. It is the smallest square that is also a sum of two (non-zero) squares: 2^5 = 3^2 + 4^2.
2. 25 is the sum of the first 5 odd numbers(= 1 + 3 + 5 + 7 + 9).
3. Couples who have been married for 25 years celebrate their Silver Wedding.
4. The Chemical Element Manganese has an atomic number of 25.
5. 25 is the number of days approximately that takes the sun to do a complete rotation on itself.

Special properties of number 24 (Today’s Date)

1. 24 is the factorial of 4 (24 = 4!).
2. 24 is an Abundant Number. In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number itself. The first few abundant numbers are 12, 18, 20, 24, 30, 36, ... There are only 21 abundant numbers less than 100, and they are all even.
3. 24 is the largest number divisible by all numbers less than its square root.
4. It is a highly composite number, having more divisors than any smaller number.
5. 24 is a semiperfect number, since adding up all the proper divisors of 24 except 4 and 8 gives 24.
6. Subtracting 1 from any of its divisors (except 1 and 2, but including itself) yields a prime number; 24 is the largest number with this property.
7. 24 is a Harshad number (number divisible by its sum of digits).
8. The product of any four consecutive numbers is divisible by 24.
9. 24 is the only nontrivial solution to the cannonball problem, that is: 1^2+2^2+3^2+...+24^2 is a perfect square (=70^2). (The trivial case is just 1^2 = 1^2.)
10. 24 is the number of Tirthankaras (in Janism)
11. 24 is the number of spokes in the Ashok Chakra
12. 24 carats represents 100% pure gold.
13. There are 24 hours in a day.
14. 24 is the number of letters in both the modern and classical Greek alphabet.
15. The Chemical Element Chromium has an atomic number of 24.

Special properties of number 23 (Today’s Date)

1. According to the birthday paradox, in a group of 23 (or more) randomly chosen people, the probability is more than 50% that some pair of them will have the same birthday. For 60 or more people, the probability is greater than 99 per cent!
2. 23 is the smallest prime number with consecutive digits.
3. 23! is 23 digits long.
4. Twenty-three is the sum of three other, consecutive, prime numbers; 5, 7 and 11. It is the first prime number showing this characteristic.
5. The sum of the first 23 primes is 874, which is divisible by 23, a property shared by few other numbers.
6. Repeat the digit 1, 23 times like this: 11,111,111,111,111,111,111,111 and you obtain a prime number.
7. Every positive whole number can be written as the sum of eight cubes (including 0^3 when necessary) except 23 (and 239). Those two numbers require 9 cubes.
8. Nobel Prize-winning economist John Forbes Nash, the inspiration for the film A Beautiful Mind, was obsessed with the number 23 and it featured prominently in his nervous breakdown. He claimed that Pope John XXIII was in fact himself, the evidence being that 23 was his favorite number. Nash also published only 23 scientific articles.
9. The axis of the planet Earth is 23.5 degrees to the vertical. The tropics of Cancer
and Capricorn are at 23.5˚ north and south respectively.
10. The Chemical Element Vanadium has an atomic number of 23.
11. Normal human sex cells have 23 chromosomes. Each parent contributes 23 chromosomes to the start of human life. The nuclei of cells in human bodies have 46 chromosomes made out of 23 pairs.