Mathematics are the result of mysterious powers which no one understands, and which the unconscious recognition of beauty must play an important part. Out of an infinity of designs a mathematician chooses one pattern for beauty’s sake and pulls it down to earth ~ Marston Morse

Mathematics can be tricky most of the time. This is a subject that is fun for some people and for some it’s the world’s hardest thing to solve. But sometimes some topics just create curiosity in everyone’s mind whether you like mathematics or not.

So, today I’m going to tell you about a topic that leaves you too in curiosity as it’s said in mathematics there is no such number that can be divided by the digits from 1 to 10 but it was only applicable till the great Mathematician Srinivasa Ramanujan discovered a number which was divisible by all the digits from 1 to 10 and this number and his discovery had left most of the mathematicians around the world in perplexed.

Srinivasa Ramanujan

Srinivasa Ramanujan was born in Erode, Tamil Nadu, India on 22nd December 1887 he was known as India’s mathematics genius. While in his childhood he did so well in his studies and made himself an able all-rounder scholar, and at an early age started working on his mathematics on the topics of arithmetic series and summing geometry. To sum up, Srinivasa Ramanujan outnumbered mathematics.

Unique number

The unique number that Srinivasa Ramanujan discovered was ‘2520’. Now that’s where all the mystery ends this is the number that can be divided by all the digits 1,2,3,4,5,6,7,8,9,10 and it is to be said that after Ramanujan no one could ever find another number that’s divisible by all these digits. That’s the reason this number is known as the most unique number.

Now you may think that 2520 is just a simple number and it’s like every other number but in reality, it’s not. That’s the reason why all the greatest mathematicians were shocked to see the results of this number.

Secret behind this unique number

I know you all were waiting for this part so here we go. This number 2520 is divisible from all the numbers 1 to 10 whether the number is odd or even leaving zero for obvious reasons.

Let’s see this table and whether all of this is true:

• 2520 ÷ 1 = 2520
• 2520 ÷ 2 = 1260
• 2520 ÷ 3 = 840
• 2520 ÷ 4 = 630
• 2520 ÷ 5 = 504
• 2520 ÷ 6 = 420
• 2520 ÷ 7 = 360
• 2520 ÷ 8 = 315
• 2520 ÷ 9 = 280
• 2520 ÷ 10 = 252

Now, what’s the first thing that came into your mind? Maybe this was so easy and it is but that’s its uniqueness that only this number is divisible from 1 to 10 and discovered this is also not easy that’s the reason no one could ever find or discover any such number which was possibly divisible by all these digits.

If someone wants to do some kind of smart work, then using prime factorization, we can write 2520 = 2³ × 3² × 5 × 7 (we can see, there are 7 prime factors). Forming suitable combinations, we see that 2520 is divisible by each of the numbers 1, 2,. . ., 10. In addition to that, 2520 is the LCM of the numbers 1, 2, . . . , 10 and hence it is the smallest number that is divisible by each of the numbers 1, 2, . . . , 10.

Next, the sum of all the digits of the number is 2 + 5 + 2 + 0 = 9, which tells us that the number is divisible by 9. Moreover, we can write 2520 as the product 2520 = 3 × 4 × 5 × 6 × 7, the product of five consecutive integers. Even we can also write 2520 = 5 × 7 × 8 × 9.

The factors of the number 2520 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260 and 2520. We can see, it is a number with 48 factors.

Anything else? Yes. Still, something is left.

A simple computation shows that 2520 can be written as a product like 7 × 30 × 12. So what? Nothing new in it. But there is something to notice. It’s like

Now, we split the numbers 2520 as 25 and 20 and take their sum. The sum will be 25 + 20 = 45. The square of 45 is 45² = 2025 and it’s just the interchange of the numbers 25 and 20!

Last but not the least, a complete revolution around a point makes 360 degrees. Naturally, it will take 7 complete revolutions to make 2520 degrees because 2520 = 7 × 360.

Your suggestions are eagerly and respectfully welcome! See you soon with a new mathematics blog that you and I call “Math1089 – Mathematics for All!“.

What made this possible?

What’s that one thing which makes this number possible to be divisible? A very simple answer is – ‘Time’ is the perfect dominance. And if I say the magic behind this number can be explained with the help of multiplication would all of you agree? Okay, let’s see the explanation of this riddle. You just have to keep in mind the Indian Hindu Year.

Considering there are 7 days in a whole week, 30 days in a month, and a total of 12 months in a year. So, if we multiply all these three numbers i.e. 7 × 30 × 12 = 2520. Surprised? That’s the sharpness of Srinivasa Ramanujan, what a great man!!

Conclusion

In particular, India has made important discoveries in many areas of mathematics whether you take Aryabhatta’s discoveries or Srinivasa Ramanujan’s discoveries. This was one of his famous works but he has also contributed to the analytical theory of numbers, infinite series, continued fractions, and elliptic functions.

So, the solution to this riddle was a proud moment for India and Mathematics.

6 Interesting Facts about Srinivasa Ramanujan

Srinivasa Ramanujan was one of the world’s greatest mathematicians. His life story, with its humble and sometimes difficult beginnings, is as interesting in its own right as his astonishing work was.

The book that started it all | Srinivasa Ramanujan had his interest in mathematics unlocked by a book. It wasn’t by a famous mathematician, and it wasn’t full of the most up-to-date work, either. The book was A Synopsis of Elementary Results in Pure and Applied Mathematics (1880, revised in 1886), by George Shoobridge Carr. The book consists solely of thousands of theorems, many presented without proofs, and those with proofs only have the briefest. Ramanujan encountered the book in 1903 when he was 15 years old. That the book was not an orderly procession of theorems all tied up with tidy proofs encouraged Ramanujan to jump in and make connections on his own. However, since the proofs included were often just one-liners, Ramanujan had a false impression of the rigor required in mathematics.

Early failures | Despite being a prodigy in mathematics, Ramanujan did not have an auspicious start to his career. He obtained a scholarship to college in 1904, but he quickly lost it by failing in nonmathematical subjects. Another try at college in Madras (now Chennai) also ended poorly when he failed his First Arts exam. It was around this time that he began his famous notebooks. He drifted through poverty until in 1910 when he got an interview with R. Ramachandra Rao, the secretary of the Indian Mathematical Society. Rao was at first doubtful about Ramanujan but eventually recognized his ability and supported him financially.

Go west, young man | Ramanujan rose in prominence among Indian mathematicians, but his colleagues felt that he needed to go to the West to come into contact with the forefront of mathematical research. Ramanujan started writing letters of introduction to professors at the University of Cambridge. His first two letters went unanswered, but his third—of January 16, 1913, to G.H. Hardy—hit its target. Ramanujan included nine pages of mathematics. Some of these results Hardy already knew; others were completely astonishing to him. A correspondence began between the two that culminated in Ramanujan coming to study under Hardy in 1914.

Get pi fast | In his notebooks, Ramanujan wrote down 17 ways to represent 1/pi as an infinite series. Series representations have been known for centuries. For example, the Gregory-Leibniz series, discovered in the 17th century is pi/4 = 1 - ⅓ + ⅕ -1/7 + … However, this series converges extremely slowly; it takes more than 600 terms to settle down at 3.14, let alone the rest of the number. Ramanujan came up with something much more elaborate that got to 1/pi faster: 1/pi = (sqrt(8)/9801) * (1103 + 659832/24591257856 + …). This series gets you to 3.141592 after the first term and adds 8 correct digits per term thereafter. This series was used in 1985 to calculate pi to more than 17 million digits even though it hadn’t yet been proven.

Taxicab numbers | In a famous anecdote, Hardy took a cab to visit Ramanujan. When he got there, he told Ramanujan that the cab’s number, 1729, was “rather a dull one.” Ramanujan said, “No, it is a very interesting number. It is the smallest number expressible as a sum of two cubes in two different ways. That is, 1729 = 1^3 + 12^3 = 9^3 + 10^3. This number is now called the Hardy-Ramanujan number, and the smallest numbers that can be expressed as the sum of two cubes in n different ways have been dubbed taxicab numbers. The next number in the sequence, the smallest number that can be expressed as the sum of two cubes in three different ways, is 87,539,319.

100/100 | Hardy came up with a scale of mathematical ability that went from 0 to 100. He put himself at 25. David Hilbert, the great German mathematician, was at 80. Ramanujan was 100. When he died in 1920 at the age of 32, Ramanujan left behind three notebooks and a sheaf of papers (the “lost notebook”). These notebooks contained thousands of results that are still inspiring mathematical work decades later.

References:

britannica.com
math1089.in