Twenty Four (24)
1. It is the smallest number to have 8 different factors. These factors are – 1, 2, 3, 4, 6, 8, 12 and 24.
2. A day has 24 hours.
3. It is a Harshad number. A number is known as Harshad number if it is divisible by the sum of its digits. 24 is exactly divisible by 2 + 4 = 6. This number was discovered by the Indian mathematician D R Kaprekar.
4. The sum of squares of first 24 natural numbers is a square number. It is the only integer except 1 with this property.
1^2 + 2^2 + --- + 24^2 = 4900 = 70^2
5. It is one of the kissing numbers in fourth dimensional space. A kissing number is defined as the number of non overlapping unit spheres that can be arranged such that each touch another given unit sphere. Kissing numbers are also known as Newton number.
6. Unlike English alphabets, Greek alphabets have 24 letters.
7. It is the product of first four consecutive numbers.
24 = 1 x 2 x 3 x 4
8. It is the first number which can be expressed in the form of 2^3q, where q is an odd prime.
24 = 2^3 x 3
9. Puzzle: - Take any four consecutive numbers. Multiply them and the answer will be divisible by 24. Example: - Let us take the four consecutive numbers 34, 35, 36 and 37.
Its product is 34 x 35 x 36 x 37 = 1585080 which when divided by 24 gives 66045 as quotient.
10. It is the product of second triangular number and second cube numbers.
24 = 3 x 8
11. It can be partioned in 1575 ways.
12. It is the sum of 4 consecutive odd numbers.
24 = 3 + 5 + 7 + 9
13. It is the fourth abundant number.
14. It is the third nonagonal number. A nonagonal number is a polynomial number that represents a nonagon. The nth nonagonal number is given by – n (7n – 5 ) / 2.
15. It is the sum of twin prime 11 and 13.
24 = 11 + 13
16. It is the largest integer that is divisible by all natural numbers less than its square root. The square root of 24 is 4.89 approximately therefore it is divisible by 1, 2, 3 and 4.
17. For any prime number greater than 3, p^2 – 1 is divisible by 24. If we take p = 7 then 7^2 – 1 = 48 is divisible by 24.
18. The atomic number of Chromium is 24.
19. The purest form of gold is 24 carat.
20. The 24th dimension is the highest dimension for which the exact "kissing number", the number of spheres that can be placed around a central sphere so that they all are touching it, is known. For the 24th dimension, the "kissing number is 196,560. Beyond the fourth dimension, only the eighth and twenty-fourth are known exactly. (From the blog of Pat Ballew)
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Dr Rajesh Kumar Thakur
1. It is the smallest number to have 8 different factors. These factors are – 1, 2, 3, 4, 6, 8, 12 and 24.
2. A day has 24 hours.
3. It is a Harshad number. A number is known as Harshad number if it is divisible by the sum of its digits. 24 is exactly divisible by 2 + 4 = 6. This number was discovered by the Indian mathematician D R Kaprekar.
4. The sum of squares of first 24 natural numbers is a square number. It is the only integer except 1 with this property.
1^2 + 2^2 + --- + 24^2 = 4900 = 70^2
5. It is one of the kissing numbers in fourth dimensional space. A kissing number is defined as the number of non overlapping unit spheres that can be arranged such that each touch another given unit sphere. Kissing numbers are also known as Newton number.
6. Unlike English alphabets, Greek alphabets have 24 letters.
7. It is the product of first four consecutive numbers.
24 = 1 x 2 x 3 x 4
8. It is the first number which can be expressed in the form of 2^3q, where q is an odd prime.
24 = 2^3 x 3
9. Puzzle: - Take any four consecutive numbers. Multiply them and the answer will be divisible by 24. Example: - Let us take the four consecutive numbers 34, 35, 36 and 37.
Its product is 34 x 35 x 36 x 37 = 1585080 which when divided by 24 gives 66045 as quotient.
10. It is the product of second triangular number and second cube numbers.
24 = 3 x 8
11. It can be partioned in 1575 ways.
12. It is the sum of 4 consecutive odd numbers.
24 = 3 + 5 + 7 + 9
13. It is the fourth abundant number.
14. It is the third nonagonal number. A nonagonal number is a polynomial number that represents a nonagon. The nth nonagonal number is given by – n (7n – 5 ) / 2.
15. It is the sum of twin prime 11 and 13.
24 = 11 + 13
16. It is the largest integer that is divisible by all natural numbers less than its square root. The square root of 24 is 4.89 approximately therefore it is divisible by 1, 2, 3 and 4.
17. For any prime number greater than 3, p^2 – 1 is divisible by 24. If we take p = 7 then 7^2 – 1 = 48 is divisible by 24.
18. The atomic number of Chromium is 24.
19. The purest form of gold is 24 carat.
20. The 24th dimension is the highest dimension for which the exact "kissing number", the number of spheres that can be placed around a central sphere so that they all are touching it, is known. For the 24th dimension, the "kissing number is 196,560. Beyond the fourth dimension, only the eighth and twenty-fourth are known exactly. (From the blog of Pat Ballew)
Send your valuable comments to
Dr Rajesh Kumar Thakur
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