# 101 Fun Facts About the Number 100

One hundred is one of the most ubiquitous numbers in life. We see it on money, best-of lists, memorials, compilations, scoring systems, and many other benchmarks. In math, percents are fractions out of 100, the most common way to measure amounts that are less than whole. 100 is used to signify large quantities because it is the square of our counting base, 10. It is also an important milestone number, like 50 and 25. Here are more curious facts and mathematical properties of the number 100.

## 24 Basic Math Facts About 100

- 100 is a perfect square since 10*10 = 100.
- The sum of the first 9 primes is 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 = 100.
- 100 is the sum of four consecutive triangular numbers: 15 + 21 + 28 + 36 = 100.
- The proper divisors of 100 are 1, 2, 4, 5, 10, 20, 25, and 50.
- The 100th triangular number is 1 + 2 + 3 + ... + 99 + 100 = 5050.
- The 100th prime number is 541.
- 100 is a Harshad Number since it is divisible by the sum of its digits: 100/(1+0+0) = 100. All powers of 10 have this property.
- 100 is the sum of the first 4 cube numbers: 1 + 8 + 27 + 64 = 100. This is consequence of the fact that 100 is the square of the 4th triangular number, 10.
- You can use four 4s to write an expression that evaluates to 100: (4/4 + 4!)*4 = 100.
- You can use five 5s to write an expression that evaluates to 100: 5! - 5 - 5 - 5 - 5 = 100.
- With six 6s you can also write an expression that equals 100: [(6+6)/6]^6 + 6*6 = 100.
- You can also write an expression that equals 100 using seven 7s: (7+7)*7 + 7/7 + 7/7 = 100.
- With eight 8s, one possible solution to the 100 problem is (8*8) + 8*(8*8 + 8)/(8 + 8) = 100.
- With nine 9s one possible solution is 9*9 + 9 + 9 + (9 + 9)/9 + (9/9) = 100. Can you find a solution with ten 10s? (Hint: You really don't need a hint for this one.)

- A googol is 10^100, a one followed by 100 zeros. The word was coined by the nephew of the American mathematican Edward Kasner. A googolplex is a one followed by a googol zeros, 10^(10^100).
- 100^100 is a number with 201 digits, ending in 200 zeros. Equivalently, it's a googol squared.
- A polygon with 100 sides is called a hectagon. The exterior angle measure of a hectagon is 176.4 degrees.
- A polyhedron with 100 faces is called a hectahedron.
- 100 can be expressed as the sum of two primes in six different ways: 3 + 97, 11 + 89, 17 + 83, 29 + 71, 41 + 59, 47 + 53.
- There are eight ways to compute 100 as a product of integers greater than 1:

2*2*5*5, 2*2*25, 4*5*5, 2*5*10, 2*50, 4*25, 5*20, 10*10. - There are only 100 prime numbers whose digits are in ascending order from left to right. Several examples are 59, 139, 239, 3457, and 12356789.
- 100 is a Leyland number since it can be expressed as x^y + y^x for some positive integers x and y greater than 1. In this case, 2^6 + 6^2 = 64 + 36 = 100.
- In Roman numerals, 100 is represented by C. This is because the "cent-" is the Latin root for one hundred.
- There are exactly 50,445,672,272,782,096,667,406,248,628 ways to split a group of 100 objects into two groups of 50.

## 26 More Facts About 100: Culture and Science

- Every country has currency denominated in units of 100 or 1/100.
*Cien Años de Soledad*(In English,*One Hundred Years of Solitude*) is a novel by the Nobel Prize-winning Colombian writer Gabriel García Márquez.- 100 degrees Celsius is the boiling point of water.
- A molecule of sodium fluoroacetate has an atomic mass of 100.0. Sodium fluoroacetate is a pesticide that occurs naturally in some plants and can be synthesized in a lab. Its chemical formula is FCH
_{2}CO_{2}Na. - The atomic number of the element fermium is 100. Fermium is a synthetic element that was first discovered in 1952, in the debris of the first hydrogen bomb test. The element is named after Enrico Fermi.
- The imaginary division between the Earth's atmosphere and outer space is called the Kármán line, and is set at a distance of 100 km above sea level.
- There are 100 tiles in the word-making board game Scrabble
- There are 100 senators in the US Senate.
- An American football field is 100 yards long.
- The most points ever scored by a single player in an NBA game is 100. This score was attained by Wilt Chamberlain in 1962 while playing for the Philadelphia Warriors.
- Some animals that can live to be at least 100 years old include humans, Galapagos tortoises, ocean quahogs (clams), bowhead whales, tuataras (lizards endemic to New Zealand), and Greenland sharks.
- "The 100" is a post-apocalyptic TV show.
- In old buildings, the door number of the bathroom used to be 100.
- There are 100 words in the Swadesh list, a list of basic words proposed by linguist Morris Swadesh for the purpose of comparing different languages.

- 100 dalmatians is one too few dogs to make a Disney movie about dalmatians.
- People who reach the age of 100 are called centenarians. A person often receives a letter from the president/queen/king/alien overlord upon reaching her 100th birthday. Women are more likely than men to reach this milestone.
- The 100th episode of
*The Simpsons*was*Sweet Seymour Skinner's Baadasssss Song.* - The 100th episode of
*Family Guy*was*Movin' Out (Brian's Song)*. - The 100th episode of
*Friends*was*The One Hundredth*. In this episode Phoebe gives birth to triplets. - The 100th episode of
*I Love Lucy*was*Lucy Cries Wolf*. In this episode Lucy tests how much Ricky loves her with a prank that backfires. - Roshashana, the Jewish New Year, is celebrated with 100 blasts of the shofar during services.
- The gestation period for tigers is 100 days on average.
- In India, Israel, and Greece you must dial 100 to reach the police, not 911.
- The Hundred Years' War is the collective term for a series of conflicts between the British and French spanning the years between 1337 and 1453, which is actually more than 100 years.
- The 100th most spoken language (by number of native speakers) is Konkani, a language spoken in India.
- Radiohead has exactly 100 songs in their nine albums.

## 23 Miscellaneous Math Facts About the Number 100

- The binary representation of one hundred is 1100100.
- In ternary (base-3), the number one hundred is represented by 10201. Curiously, 10201 in base-10 is the square of 101.
- In base-5, one hundred is represented by 400. It just so happens that 400 is the base-10 square of 20.
- In base-6, one hundred is represented by 244.
- In octal, one hundred is 144, another string that represents a square number in base-10.
- And in hexadecimal (base-16) one hundred is represented by 64, yet another base-10 square.
- 100 minutes is 1 hour and 40 minutes.
- 100 days is 14 weeks and 2 days.
- A circle with an area of 100 has a diameter of 11.28379.
- The sum 1^1 + 2^2 + 3^3 + ... + 98^98 + 99^99 + 100^100 equals

100,371,115,746,176,445,351,701,210,713,361,941,528,546,861,949,073,514,542,015,172,437,236,580,034,634,746,971,244,943,788,132,460,150,776,779,198,800,002,366,059,871,900,041,784,732,217,539,059,306,483,834,977,865,973,576,751,345,853,385,981,719,448,969,027,641,920. This is a number with 201 digits. - The smallest number that has exactly 100 factors is 45,360.
- The sum of the first 100 prime numbers is 24,133. As it turns out, 24,133 is also a prime number.
- The product of the first 100 prime numbers is 4,711,930,799,906,184,953,162,487,834,760,260,422,020,574,773,409,675,520,188,634,839,616,415,335,845,034,221,205,289,256,705,544,681,972,439,104,097,777,157,991,804,380,284,218,315,038,719,444,943,990,492,579,030,720,635,990,538,452,312,528,339,864,352,999,310,398,481,791,730,017,201,031,090. This is a number with 220 digits.
- Starting with 1 as the first Fibonacci number, 1 as the second Fibonacci number, 2 as the third Fibonacci number, etc., the 100th Fibonacci number is 354,224,848,179,261,915,075.
- One hundred factorial, written as 100!, is equal to 93,326,215,443,944,152,681,699,238,856,266,700,490,715,968,264,381,621,468,592,963,895,217,599,993,229,915,608,941,463,976,156,518,286,253,697,920,827,223,758,251,185,210,916,864,000,000,000,000,000,000,000,000. This is a number with 158 digits.
- There 444,793 ways to partition 100 items into groups of different sizes. For example, {1, 2, 97} and {3, 15, 21, 30, 31} are two such partitions of 100 into different sized parts.
- There are exactly 100 ways to partition 13 items into 2 or more parts.
- Starting with 3 as the first digit of π, the 100th digit of π is 7.
- Starting with 2 as the first digit of e, the 100th digit of e is also 7.
- There are 744 integer solutions to the equation a
^{2}+ b^{2}+ c^{2}+ d^{2}= 100. - There are 30 integer solutions to the equation a
^{2}+ b^{2}+ c^{2}= 100. - There are only two numbers whose proper factors add up to one hundred, 124 and 194. (Proper factors are divisors less than the number itself.)
- There is no number such that all of its factors (including itself) add up to 100.

## 15 Random Facts About the Number 100

- There are about 100 calories in 28 baby carrots.
- There are about 100 calories in a small baked potato.
- There are about 100 calories in a single slice of whole wheat bread.
- A human farts about 100 times a week on average.
- Washington DC is about 100 miles from Wilmington, Delaware and about 100 miles from Richmond, Virginia.
- Oklahoma City and Tulsa are about 100 miles apart.
- The island nation of Malta is about 100 km off the coast of Sicily.
- In the year 100 AD somebody in China invented the wheelbarrow.
- In the year 100 AD somebody wrote the Gospel of John.
- In the year 100 AD Sextus Julius Frontinus and Emperor Trajan became Roman consuls.
- Hundred is a town in West Virginia. It got its name from a husband and wife pair of early settlers who both lived past the age of 100.
- It takes between 35 and 40 seconds to count to 100 out loud speaking quickly.
- It takes between 75 and 80 seconds to count to 100 out loud speaking at a normal pace.
- Counting from 1 to 100 makes you say 203 syllables.
- There are exactly 100 years between your third birthday and 103rd birthday.

## 13 Bits of Trivia About 100

- 100 is the smallest three-digit number.
- There are 50,613,244,155,051,856 possible ways to score exactly 100 points in a game of bowling.
- There are 100 grid points on each Battleship board game panel.
- The state of North Carolina has exactly 100 counties.
- Despite the name, centipedes do not have 100 legs. All centipedes have an odd number of pairs of legs, which means the total number is never divisible by 4. A millipede, however, can have 100 legs. But despite its name, the highest number of legs ever found on a millipede was 750, not 1000.
- There are 100 centimeters in a meter.
- There are 100 square meters in an are, and 100 ares in a hectare.
- When rolling 100 regular 6-sided dice and adding up all the numbers, the average sum is 350.
- In the Hawaiian language, one hundred is "ho`okahi hanele."
- In the Basque language, one hundred is "ehun."
- In the Finnish language, one hundred is "sata."
- The unicameral legislature of Latvia has 100 seats.
- If you write every number from 1 to 100, you will write 912 digits.

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## 13 comments

Awesome facts!

Neat stuff -- as usual. I just take sightings of "100" for granted, but it is amazing how ubiquitous the number is. Good thing you covered the topic before Copycatman could compose his/her own number facts article. Knowing him/her it would be filled with such deep observations as "100 is the 100th positive number" and "100 is a number with one 1 and two 0s" lol.

Interesting article. Is there anything in particular that made you pick the number 100, or did you just pick it because it was a nice clean number?

Oh, alright.

100 pairs of frogs each beget 100 tadpoles. The tadpoles become frogs and pair off and each pair begets 100 tadpoles in a new generation. How many tadpoles and frogs total? Thanks.

please help solve; problem#100; what is sum of all four-digit numbers whose squared digits sum to 100?

Interesting article with a lot of things I wouldn't have thought about.

Number trivia is anything but trivial. What a fun and thought-provoking read!

13