# Fun Facts About the Number 120

TR Smith is a product designer and former teacher who uses math in her work every day.

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One hundred twenty is a highly divisible number often encountered in Christian and Jewish religious traditions. Up until the 1400s, it was the number 120 rather than 100 that was known as a "hundred" in Germanic cultures. The number 120 also has many wonderful mathematical properties. For example, it is the number of ways to pick three objects out of a set of 10 objects without regard to order. There are also 120 ways to pick two objects out of a set of 16 objects disregarding order. Here are some other interesting, useful, and useless facts about the number 120.

## 13 Math Facts about 120

• 120 is the sum of the first 15 whole numbers, making it the 15th triangular number. 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 = 120.
• 120 is also the sum of the first eight triangular numbers, making it the eighth tetrahedral number. 1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 = 120.
• 120 is also the eighth hexagonal number.
• 120 is the product of the first five positive whole numbers, "5!" aka five factorial. 1 x 2 x 3 x 4 x 5 = 120.
• There are 12 ways to write 120 as the sum of two primes.
• The sum of the factors of 120 is 360. This means 120 is a "three-perfect" number, a number whose factor sum is three times the number itself.
• There are four numbers whose factor sum is 120: 54, 56, 87, and 95.
• 120 is known as a highly composite number, meaning it has more factors than any number below it.
• The prime factorization of 120 is 2 x 2 x 2 x 3 x 5, and the sum of the prime factors is 14.
• 120^120 is a number with 250 digits.
• 120! is a number with 199 digits.
• 120 written in binary is 1111000.
• The string "120" in ternary represents the number eighteen, which is a lucky number in Judaism.

Scene from "Homer vs. Patty and Selma," the 120th episode of The Simpsons.

## 15 Facts About 120 in Religion, Culture, and Science

• "120" is a Turkish film about World War I.
• In the Bible, Moses lived to the age of 120.
• A common Jewish benediction is to say "May you live to be 120."
• In the Biblical book II Chronicles, the height of the temple is 120 cubits.
• In the Biblical book Daniel, Kind Darius establishes 120 satraps (princes or nobles) over his kingdom.
• Many significant numbers in the Bible are multiples of 120 or 12. For instance, in Revelations the number of saved people is 144,000.
• The legislative body of Israel, called the Knesset, has 120 seats.
• The 1960s television series "Batman" ran for a total of 120 episodes.
• The 120th episode of The Simpsons was "Homer vs. Patty and Selma."
• The 120th episode of Seinfeld was "The Gum."
• In the NBA, the official regulation height of a basketball hoop is 120 inches.
• The Marquis de Sade wrote "120 Days of Sodom" while imprisoned in the Bastille.
• The average gestation period of a bushbaby is 120 days.
• Dashavatara Ganjifa is a card game played in India with a special deck of 12 cards. The cards are divided into 10 suits and 12 ranks; each suit represents an avatar of the deity Vishnu. Like traditional Indian playing cards, they are circular rather than rectangular.
• Jeanne Calment is the only person documented to have lived past the age of 120. She reached the age of 122.

## 12 More Random Math Facts About 120

• The angles of a regular hexagon are 120 degrees.
• A polygon with 120 sides is called either a dodecacontagon or hecatonicosagon, but most people just write "120-gon."
• There are 23 Pythagorean triples that contain 120 as either a leg or hypotenuse.
• There are 18 quadratic residues modulo 120: 0, 1, 4, 9, 16, 24, 25, 36, 40, 49, 60, 64, 76, 81, 84, 96, 100, and 105.
• 120 is a Harshad or Niven number, meaning it is divisible by the sum of its digits. 120 รท (1 + 2 + 0) = 40.
• 120 is the seventh term in the sequence 0, 1, 2, 6, 16, 44, 120, 328, 896, 2448, 6688, 18272... Each term in this sequence, starting with the third term, is two times the sum of the two previous terms.
• The number 120 occurs six times in Pascal's Triangle.
• 120 is the 29th term in the sequence 4, 6, 9, 12, 15, 18, 21, 26, 30, 34, 39, 42, 45, 50, 56, 60, 64, 69, 72, 76, 81, 86, 93, 99, 102, 105, 108, 111, 120, 129,... The terms in this sequence are the midpoints of the prime number sequence, or in other words, each is the average of two consecutive odd primes.
• In Roman numerals, 120 is written as CXX.
• There are 120 ways to partition 35 into subsets with a maximum size of three. Equivalently, if you have a currency system with \$1, \$2, and \$3 bills, there are 120 ways to make change for \$35 using only \$1, \$2, and \$3 bills.
• If P, Q, and R are positive numbers, and P^2 + PQ + Q^2 = R^2, then a triangle with sides P, Q, and R has an angle of exactly 120 degrees.
• 120 is the product of three consecutive integers, 4 x 5 x 6 = 120.

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