416

416 = 2⁵ x 13.

416 is the number of subsets of the 15th roots of unity that add up to a real number.

416 has a representation as a sum of two squares: 416 = 4² + 20².

416 is a number with exactly 12 divisors: 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416.


416 is the area code for the city of Toronto. It is one of the original 86 area codes from 1947.

Episode 416 (4th season, 16th episode) of the TV series Numb3rs was titled "Atomic No. 33" and included references to non-Newtonian fluids, the Riemann zeta function, and Bayesian network analysis.

Sources: What's Special About This Number?; The Math Behind Numb3rs

63

63 = 3² x 7.

63 = 6² + 3³ = 2⁶ – 1.

63 is the smallest number such that the common alphabetical value of its representation in Roman numerals is equal to itself: LXIII -- 12 + 24 + 9 + 9 + 9 = 63.

63 is a Harshad (or Niven) number; that is, it is divisible by the sum of its digits.

63 is the number of partially ordered sets of 5 elements.

63 is 333 in base 4.

M63 is a galaxy, known as the Sunflower Galaxy, in the constellation Canes Venatici.

Source: Number Gossip

145

145 = 5 x 29.

145 = 1! + 4! + 5! The only other numbers that are the sum of the factorials of their digits are 1, 2, and 40,585. These numbers are known as factorions.

145 is a pentagonal number and a centered square number.

145 is the sum of two squares in two different ways: 145 = 12² + 1² = 8² + 9².

145 is the hypotenuse of two primitive Pythagorean triples: 145² = 17² + 144² = 24² + 143².

Ted Williams hit 31 home runs and had 145 RBI as a rookie in 1939.

Source: Wolfram MathWorld

118

118 = 2 x 59.

118 is the smallest number that can be written as the sum of four triples, whose products are all equal: 118 = 14 + 50 + 54 = 15 + 40 + 63 = 18 + 30 + 70 = 21 + 25 + 72. The product of each triple is 37,800.

118 is the smallest three-digit composite number, all of whose other digit permutations are prime numbers: 181 and 811 are both prime.

118 is the sum of three positive cubes: 118 = 4³ + 3³ + 3³.

118 Peitho is an asteroid that was discovered in 1872.

Source: Number Gossip

74

74 = 37 x 2.

74 = 17 + 18 + 19 + 20.

74 is a hungry number. The kth hungry number is the smallest number n such that 2ⁿ contains the first k digits of the decimal expansion of pi: 5, 17, 74, 144, 144, 2003, . . . . The first number is 5 because 2⁵ is 32, which contains 3, the first digit of pi. They were named hungry numbers because they try to eat as much "pi" as possible.

74 has a representation as a sum of two squares: 74 = 5² + 7².

74 is the atomic number of tungsten.

Source: Number Gossip

56

56 = 2³ x 7.

56 is a pronic number because it is the product of two consecutive numbers: 7 x 8 = 56.

56 is the sum of the first six triangular numbers: 1 + 3 + .6 + 10 + 15 + 21 = 56. Hence, it is a tetrahedral number, the number of balls you can put in a triangular pyramid: 1, 4, 10, 20, 35, 56, 84, 120, . . .

56 is the sum of six consecutive prime numbers: 3 + 5 + 7 + 11 + 13 + 17 = 56.


56 men signed the Declaration of Independence in 1776, which led to the formation of the United States of America.

Source: Number Gossip

1111

1111 = 11 x 101.

1111 is the sum of the digits of the first 100 primes.

1111 is a number that cannot be written as a sum of three squares.

1111 is a divisor of 100² - 1.

1111 is n³ + n² + n + 1, for n = 10.

1111 is 787 in base 12.

Armistice Day, Nov. 11 (11/11), is the anniversary of the symbolic end of World War I in 1918, when the leaders of several countries signed an agreement on the 11th hour of the 11th day of the 11th month to cease hostilities.

Source: Number Gossip