2520 – The Strange Number

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

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Mathematics is all about numbers and few numbers are really strange! Here, we will consider one such number, 2520. 2520 is the natural number following 2519 and preceding 2521.

But why we should consider this number? Wait for some time to know more about it. The number 2520 looks like a normal number like others, but it is not.

What is so important in this number? First of all, it is an even number. Second, it is divisible by all the numbers from 1 to 10, whether they are odd or even! See below:

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

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 which 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 number 2520 as 25 and 20 and take their sum. The sum will be 25 + 20 = 45. 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.

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