3600

3600 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5.

3600 is a perfect square (A159991). It is both the sum and the difference of two primes (A106575).

3600 has a representation as a sum of two squares: 3600 = 36² + 48².

3600 is the order of a perfect group.

3600 is 11221100 in base 3 (A033001). It is 2100 in base 12 and 1100 in base 15.

3600 is a concentric hexadecagonal number (A195146).

3600 is the number of seconds in an hour.

Source: Number Gossip

1521

1521 = 3 x 3 x 13 x 13.

1521 is a perfect square: 1521 = 39².

1521 is the smallest number that can be written as the sum of four distinct cubes in three ways: 1521 = 11³ + 5³ + 4³ + 1³ = 10³ + 8³ + 2³ + 1³ = 9³ + 8³ + 6³ + 4³.

1521 has a representation as a sum of two squares: 1521 = 15² + 36².

1521 is a divisor of 22³ - 1.

1521 is a centered octagonal number.

Source: What's Special About This Number?

121

121 = 11 x 11.

121 is the smallest multidigit palindromic square. It is also the smallest palindromic composite such that some permutation of digits is prime. It is the only odd palindromic square with an odd number of digits that is divisible by a palindromic prime number with an even number of digits.

121 is a perfect square. It is also a centered octagonal number and a centered dodecagonal number.

Every number greater than 121 is the sum of distinct primes of the form 4n + 1.

121 is 11111 in base 3.

121 is the maximum number of regions into which 15 lines divide a plane.

121 can be expressed as the sum of a prime and its reversal for exactly three distinct primes: 121 = 29 + 92 = 47 + 74 = 83 + 38.

121 = 1 + 3¹ + 3² + 3³ + 3⁴.

121 is the number of points required to win a standard game of cribbage.

Source: Prime Curios!

361

361 = 19 x 19.

361 is a centered triangular number (A005448). It is also a centered octagonal number (A016754) and a centered decagonal number (A062786).

The representations of 361 in bases 2, 3, 4, 5, 6, 8, 9, and 10 all end in 1. It is 551 in base 8 and 441 in base 9. It is 121 in base 18.

361 is a square that remains a square when the last digits is removed (A023110).

361 and 361² (130321) have the same digit sum (A058369): 3 + 6 + 1 = 10 = 1 + 3 + 0 + 3 + 2 + 1.

The game of Go is played on a grid of 19 x 19 lines, which produces 361 intersections on the game board.

Source: On-Line Encyclopedia of Integer Sequences

841

841 = 29 x 29.

841 is a centered square number. It is also a centered heptagonal number and a centered octagonal number.

841 has a representation as a sum of two squares: 841 = 20² + 21². It is the sum of two consecutive squares.

841 is the hypotenuse of a primitive Pythagorean triple: 841² = 41² + 840².

841 is the smallest 3-digit square whose digits are decreasing.

841 is the smallest binary prime square. It's a perfect square whose binary representation (1101001001) considered as a decimal is a prime number.

841 is a divisor of 41⁴ - 1.

Source: Number Gossip

225

225 = 3² x 5².

225 = 15². 225 is the smallest square that starts with two identical digits.

225 is the smallest square whose external digits (25) form a square, and whose internal digits (2) form a prime.

225 is the only three-digit square with all prime digits.

225 has a representation as a sum of two squares: 225 = 9² + 12².

225 is a divisor of 26² - 1.

225 is an octagonal number. It is also a centered octagonal number.

A Scrabble board has 225 squares.

Source: Number Gossip

324

324 = 2² x 3⁴.

324 is a perfect square: 324 = 18².

324 is the smallest untouchable square. Untouchable numbers are those that are not the sum of the proper divisors of any number.

324 is the largest possible product of positive integers with sum 16.

324 Bamberga, discovered in 1892, is one of the largest asteroids in the main belt.

Source: Number Gossip

196

196 = 2² x 7².

196 is the smallest square that contains a multidigit prime number as a substring.

196 = 14² is a perfect square.

196 is the difference of two square numbers: 196 = 50² - 48².

The consecutive squares 13² = 169 and 14² = 196 use the same digits; 31² = 961 also uses the same digits.

196 has a unique representation as a sum of three squares: 196 = 4² + 6² + 12².

196 is a pentagonal pyramidal number and a heptagonal pyramidal number.

It is conjectured that 196 is the lowest Lychrel number. It is the lowest number not known to produce a palindrome by repeated reversal and addition. The algorithm has been tested to more than 246 million digits without finding a palindrome, but no one has ever proved that it will never produce one.

The Mercedes-Benz W196 was an entry in the 1954 and 1955 Formula One car racing series, winning 9 of 12 races.

Source: Number Gossip

289

289 = 17².

289 is the largest 3-digit square with increasing digits.

289 has a representation as a sum of two squares: 289 = 8² + 15².

289 is the hypotenuse of a primitive Pythagorean triple: 289² = 161² + 240².

289 is a centered octagonal number.

The Ford Mustang 289 was a high-performance version of the car in the 1960s.

Source: Number Gossip

576

576 = 2⁶ x 3².

576 has a unique representation as a sum of three squares: 576 = 8² + 16² + 16².

576 is the number of 4 x 4 Latin squares.

576 is the smallest square such that it remains a square when its leading digit is increased by 1: 676 = 26².

576 = (2 + 3 + 5 + 7 + 11)² - (2² + 3² + 5² + 7² + 11²).

New Balance produces a 576 line of fitness walking shoes.

Source: Number Gossip

100

100 = 2² x 5².

100 has a representation as a sum of two squares: 100 = 6² + 8².

100 is the sum of the first four cubes: 100 = 1³ + 2³ + 3³ + 4³. It is the smallest square that is the sum of consecutive cubes.

100 is the sum of the 9th and 10th triangular numbers: 100 = 45 + 55.

100 is the sum of the first 10 odd numbers: 100 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19.

The first three primes add to 10, and the first 3² primes add to 10² = 100.

The Romans wrote 100 as C. This is an abbreviation for the Latin word centum. A cent is a hundredth of a dollar, and a centime was a hundredth of a franc.

Source: Prime Curios!

36

36 = 2² x 3². It is a perfect square.

36 is 100100 in base 2 (binary). It is 44 in base 8.

36 has a unique representation as a sum of three squares: 36 = 2² + 4² + 4².

36 is the smallest number with four representations as a sum of two distinct primes: 36 = 5 + 31 = 7 + 29 = 13 + 23 = 17 + 19.

36 is the 8th triangular number (the sum of the first eight numbers). There are not many numbers that are both square and triangular. The first four are 1, 36, 1225, and 41616.

36 is the sum of the first three cubes: 1³ + 2³ + 3³.

36 is the smallest number to have nine different factors: 1, 2, 3, 4, 6, 9, 12, 18, and 36.

William Shakespeare wrote 36 plays.

Source: Phillips, R. 1994 Numbers: Facts, Figures and Fiction. Cambridge University Press.

400

400 = 2⁴ x 5².

400 = 20², a perfect square.

400 = 7⁰ + 7¹ + 7² + 7³. Hence, 400 is 1111 in base 7.

400 has a representation as a sum of two squares: 400 = 12² + 16².

A full circle is 360 degrees or 400 grads.

Years divisible by 400 are leap years, following adoption of the current Gregorian calendar.

Source: Numeropedia

676

676 = 2² x 13².

676 = 26², a perfect square.

676 is the smallest palindromic square whose square root is not palindromic.

676 has a representation as a sum of two squares: 676 = 10² + 24².

676 is a divisor of 99⁴ - 1.

676 is 1010100100 in base 2 (binary).

676 Melitta is an asteroid discovered in 1909.

Source: Number Gossip

25

25 = 5², a perfect square.

25 has a representation as a sum of two squares: 25 = 3² + 4². It is the smallest square that can be written as a sum of two squares.

25 is the hypotenuse of a primitive Pythagorean triple: 25² = 7² + 24².

25 is the sum of the first five odd numbers: 25 = 1 + 3 + 5 + 7 + 9.

25 = 3 + 4 + 5 + 6 + 7.

25 is an octahedral number.

Every square number is the sum of two triangular numbers: 25 = 10 + 15.

Pachisi, the Hindu word for 25, is one of the national games of India.

Source: Phillips, R. 1994. Numbers: Facts, Figures and Fiction. Cambridge University Press.

144

144 = 2⁴ x 3².

144² = 12², a perfect square. If you reverse the digits, 21² = 441.

144 has a unique representation as a sum of three squares: 144 = 4² + 8² + 8².

144 is a square number. Divide it by 4 and you get 36, which is also square. Does this happen with any other square numbers?

144 is the 12th Fibonacci number.

144 is 99 in base 15.

The interior angles in a regular decagon measure 144 degrees. In counting objects, 144 is called a gross (a dozen dozens).

Source: WolframAlpha

961

961 = 31². It is a perfect square.

961 is the largest square with strictly decreasing digits. It is also the largest prime power of a prime with strictly decreasing digits.

The digits of 961 can be rearranged to give two other squares: 169 = 13² and 196 = 14².

961 is 12321 in base 5 and 4241 in base 6.

961 beer is brewed in Beirut, Lebanon.

Source: Number Gossip

900

900 = 2² x 3² x 5².

900 is a square number: 30 x 30 = 900.

900 is the smallest square that is the sum of different primes by using all ten digits: 900 = 503 + 241 + 89 + 67 = 509 + 283 + 61 + 47.

900 has a base 5 representation (12100) that begins with its base 9 representation (1210). Its base 7 representation is 2424.

900 has a representation as a sum of two squares: 900 = 18² + 24².


900 is the sum (in degrees) of the internal angles of a heptagon.

Source: Prime Curios!

784

784 = 2⁴ x 7².

784 is a square number: 28 x 28 = 784.

784 is the square of the sum of the first seven integers: (1 + 2 + 3 + 4 + 5 + 6 + 7)² = 784.

784 is the sum of the first seven cubes: 1³ + 2³ + 3³ + 4³ + 5³ + 6³+ 7³ = 784.

784 is 1002001 in base 3 and 3344 in base 6.

Asteroid 784 Pickeringia was discovered in 1914.

Source: Numeropedia

484

484 = 2² x 11²

484 is a square number: 22 x 22 = 484.

484 is a palindrome in base 3 (12221) and in base 10.

484 has exactly nine divisors: 1, 2, 4, 11, 22, 44, 121, 242, 484.


Juliett 484 was a Soviet guided-missile submarine that eventually ended up on display at the Russian Sub Museum in Providence, R.I.

Source: The Positive Integers