Kaprekar's Constant | Brilliant Math & Science Wiki (2024)

FAQs

Which is the rarest number? ›

Other examples of rare numbers are 65, 621770, 281089082, 2022652202, 868591084757, 872546974178 … (Sequence A035519 of OEIS). If we consider palindromic rare numbers, there are infinitely many rare numbers.

The mystery is this: first, take any three digit number, where the first and last digits differ by two or more and reverse the number to produce a new one. Then subtract the smaller from the larger producing another new number. If you reverse this number and this time add the two, the result will always be 1089.

Kaprekar constant, or 6174, is a constant that arises when we take a 4-digit integer, form the largest and smallest numbers from its digits, and then subtract these two numbers. Continuing with this process of forming and subtracting, we will always arrive at the number 6174.

Kaprekar's Constant is used in cryptography to generate random numbers for encryption and decryption purposes.

In fact, many will say that infinity is the final answer to the question “what is the last number?” But, infinity isn't actually a number. Instead, infinity is an abstract concept that describes a quantity that never ends and is unbounded. In math, you can think of infinity like a highway that goes on forever.

The first few weird numbers are 70, 836, 4030, 5830, 7192, 7912, 9272, 10430, ... (OEIS A006037). An infinite number of weird numbers are known to exist, and the sequence of weird numbers has positive Schnirelmann density. (Sloane).

To the world of physics, 137 is synonymous with the fine structure constant. This constant, represented as approximately 1/137.03599913, gauges the strength of the electromagnetic force, according to the National Institute of Standards and Technology.

A mystery number is a number that can be expressed as the sum of two numbers and those two numbers should be the reverse of each other. Examples: Input : n = 121. Output : 29 92.

A number is perfect if all of its factors, including 1 but excluding itself, perfectly add up to the number you began with. 6, for example, is perfect, because its factors — 3, 2, and 1 — all sum up to 6. 28 is perfect too: 14, 7, 4, 2, and 1 add up to 28.

e, known as Euler's number, is approximately 2.71828 and is another nonrepeating, nonterminating number. This number is the natural limit for many science and economics applications. 10¹⁰⁰ is a Googol. You can write out the entire number with a 1 followed by 100 zeros.

What is the most powerful number in mathematics? ›

Pi. For all relevant purposes, it is the strongest number ever to be used by mankind. Pi. The ratio of circumference of a circle to its diameter.

Simply put, pi is weird. Mathematicians call it a "transcendental number" because its value cannot be calculated by any combination of addition, subtraction, multiplication, division, and square root extraction.

The number 6174 is a really mysterious number. At first glance, it might not seem so obvious. But as we are about to see, anyone who can subtract can uncover the mystery that makes 6174 so special.

In 1949, Indian mathematician D. R. Kaprekar, discovered the mysterious beauty of 6174 after devising a process that we now know as Kaprekar's operation. The operation: start with any four-digit number that is made up of least two different digits, including zero.

Exactly 77 4-digit numbers, namely 1000, 1011, 1101, 1110, 1111, 1112, 1121, 1211, ... (OEIS A069746), reach 0, while the remainder give 6174 in at most 8 iterations. The value 6174 is sometimes known as Kaprekar's constant (Deutsch and Goldman 2004).

The number 1

It's the only number divisible by exactly one positive integer (itself, 1). It's the only positive integer that's neither prime nor composite.

It is the highest single-digit number, and any number multiplied by 9 will always result in a number whose digits add up to 9. Additionally, the number 9 is the sum of the first three square numbers (1² + 2² + 3² = 9) and the sum of the first three cube numbers (1³ + 2³ + 3³ = 36).

“Number 0 holds the utmost value.” It was invented (symbol first used) by Brahmagupta. Later, by Aryabhata. Any other number when multiplied with 0, becomes 0.