Sunday, January 31, 2016

Mathematically 75

Seventy Five (75)

1. It is also called three quarter. 3/ 4 = 75%

2. It is one less than the sum of squares of its digit.
75 = 7^2 + 5^2 – 1

3. It can be expressed as the sum of 10 consecutive primes beginning from 3.
75 = 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12

4. It is a nonagonal number.

5. It is a pentagonal pyramid number. A pentagonal pyrammdal number is a figurarive number that represents the number of objects in a pyramid with pentagonal base.
75 = 1 + 6 + 18 + 40

6. The atomic number of Rbenium is 75.

7. It is a Keith number. A Keith numbers run like a Fibonacci sequence. 75 has its digit 7 and 5. If we start to form a sequence with the digit 75 and go on finding the next number by adding the previous two as done in Fibonacci sequence we get 75.
7, 5 , 12, 17, 29, 46, 75.. It is named after Mike Keith who discovered this number in 1987

8. It is a Self-number. A self-number is an integer which in a given base cannot be generated by any other integer added to the sum of that other integer’s digit.

Example:- 21 is not a self-number as it can be generated by 15 and sum of tis digit 1 and 5, whereas 20 is a self-number as it cannot be generated by any such numbers.

9. A diamond anniversary is celebrated after every 75 years.

10. The Proper divisor of 75 are - 1, 3, 5, 15, 25 whose sum is a perfect square
1 + 3 + 5 + 15 + 25 = 49 = 7^2
Moreover , its product
1 x 3 x 5 x 15 x 25 = 5625 = 75^2
is also a square.

11. 2^75 + 75 is a prime


Dr Rajesh Kumar Thakur

No comments:

Post a Comment

November 2, 2024