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Click on number to see Concepts connected with it. 0Can be partitioned 1 way.n/a


1Can be partitioned 1 way.n/a


2Can be partitioned 2 ways.PrimeThe 3th Fibonacci Number.The 1st Mersenne prime number.


3Can be partitioned 3 ways.PrimeThe 2nd mersenne number.triangular numberThe 4th Fibonacci Number.The 1st Delannoy Number.


4Can be partitioned 5 ways.2x2Square Number


5Can be partitioned 7 ways.PrimeThe 8th Fibonacci Number.The 3rd catalan number.


6Can be partitioned 11 ways.2x3The 3rd triangular number.The 2nd hexagonal number.The 2nd Schröder number.


7Can be partitioned 15 ways.The 4th prime number.The 3rd Mersenne prime number.The 4th mersenne number.The 4th odd number.The 4th Lucas number.The 3rd lucky number.Sum of the first 4 Fibonacci numbers= 1 + 1 + 2 + 3 = 7Difference of the first two cube numbers = 23 - 13 = 8 - 1 = 7Sum of the 2nd odd & 2nd even numbers = 3 + 4 = 7Sum of the 1st & 3rd prime numbers= 2 + 5 = 7Sum of the 1st & 3rd factorials= 1 + 6 = 7Sum of the 1st & 3rd triangular numbers= 1 + 6 = 7


8Can be partitioned 22 ways.2x2x2The 5th Fibonacci Number.


9Can be partitioned 30 ways.3x3The 5th odd number.The 4th composite number.The 2nd octagonal pyramidal number.
(sum of 1st two octagonal #s = 1+ 8 = 9) The 4th lucky number.Sum of the first two cube numbers= 1 + 8 = 9Sum of the first three odd numbers.Sum of the first three factorials= 1 + 2 + 6 = 9


10Can be partitioned 42 ways.2x5The 5th even number.The 5th composite number.The 4th triangular number.
(Sum of the 1st four numbers = 1 + 2 + 3 + 4 = 10)The 3rd tetrahedral number.
(Sum of the 1st three triangular numbers = 1 + 3 + 6 = 10)Product of the 1st even & 3rd odd numbers = 2 x 5 = 10Product of the 1st & 3rd prime numbers= 2 x 5 = 10Product of the 3rd & 5th Fibonacci numbers= 2 x 5 = 10Sum of the 1st three prime numbers = 2 + 3 + 5 = 10Sum of the 3rd, 4th, 5th Fibonacci numbers= 2 + 3 + 5 = 10Sum of the 1st & 3rd Square Numbers= 12 + 32 = 1 + 9 = 10Sum of the 1st & 4th even numbers = 2 + 8 = 10Sum of the 2nd & 4th odd numbers = 3 + 7 = 10Sum of the 2nd & 3rd,(2n - 1): 3 + 7 = 10Sum of the 2nd & 3rd even numbers = 4 + 6 = 10


11Can be partitioned 56 ways.PrimeThe 4th super catalan number


12Can be partitioned 77 ways.2x2x3The 1st abundant number


13Can be partitioned 101 ways.The 6th prime number.The 7th Fibonacci number.The 7th odd number.The 5th lucky number.The 3rd centered Square Number.The 2nd Delannoy Number.Sum of the 2nd & 3rd Square Numbers= 4 + 9 = 13Sum of the 1st perfect number & 4th prime number= 6 + 7 = 13The hypotenuse of the Pythagorean 5-12-13 triangle= 13


14Can be partitioned 135 ways.2x7The 7th even number.The 7th composite number.The 4th catalan number.The 3rd pyramidal number = 1, 5, 14Product of the 1st even & 4th odd numbers = 2 x 7 = 14Sum of the 1st, 2nd, & 4th triangular numbers= 1 + 3 + 10 = 14Sum of the 1st, 3rd, and 4th prime numbers= 2 + 5 + 7 = 14Sum of the 1st and 7th Fibonacci numbers= 1 + 13 = 14Sum of the 1st & 6th even numbers = 2 + 12 = 14Sum of the 2nd & 5th even numbers = 4 + 10 = 14Sum of the 3rd & 4th even numbers = 6 + 8 = 14Sum of the 2nd, 3rd, 4th, 5th numbers = 2 + 3 + 4 + 5 = 14


15Can be partitioned 176 ways.3x5The 5th triangular number.The 3rd hexagonal number.The 4th mersenne number.


16Can be partitioned 231 ways.2x2x2x2Square NumberThe 3rd centered pentagonal number.The 2nd truncated tetrahedal number.


17Can be partitioned 297 ways.Prime


18Can be partitioned 385 ways.2x3x3Pentagonal Pyramidal NumberThe 3rd heptagonal number.The 2nd abundant number


19Can be partitioned 490 ways.PrimeThe 4th centered triangular number.The 3rd octahedral number.


20Can be partitioned 627 ways.2x2x5The 1st abundant number.


21Can be partitioned 792 ways.3x7triangular numberThe 3rd octagonal number.The 8th Fibonacci Number.


22Can be partitioned 1002 ways.2x11Twenty-two is the number of writable regular polygons in an Euclidiean circle: 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360. These are twenty-two of the twenty-four dividers of 360, the two first, 1 and 2, not defining polygons.The 3rd Schröder number.


23Can be partitioned 1255 ways.Prime Every positive whole number can be written as the sum of eight cubes (including 0^3 when necessary) EXCEPT 23 and 239. Those two numbers require 9 cubes.


24Can be partitioned 1575 ways.2x2x2x3The 3rd nonagonal number.The 3rd abundant number.Product of the 1st and 6th even numbers = 2 x 12 = 24The 12th even number = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24Product of the 1st and 6th even numbers = 2 x 12 = 24Product of the 2nd and 3rd even numbers = 4 x 6 = 24Product of the 1st composite & 1st perfect number 4 x 6 = 24Product of the 2nd triangular & 2nd cube numbers = 3 x 8 = 24Sum of the 5th and 6th prime numbers 11 + 13 = 24The 4th abundant number= 12, 18, 20, 24Factorial 4 = 4! = 4 x 3 x 2 x 1 = 24


25Can be partitioned 1958 ways.5x5The 13th odd number.The 5th Square Number.The 4th centered Square Number.Sum of the first 5 odd numbers.Sum of the 3rd and 4th Square Numbers = 9+16=25
(Pythagorean 3-4-5 right triangle)


26Can be partitioned 2436 ways.2x13The 13th even number.The 3rd heptagonal pyramidal number.Product of the 1st even and 7th odd numbers = 2 x 13 = 26Sum of the 1st & 5th Square Numbers = 12 + 52 = 1 + 25 = 26Sum of the 6th & 7th even numbers = 12 + 14 = 26Sum of the 5th, 6th, and 7th Fibonacci numbers = 5 + 8 + 13 = 26Sum of the 5th through 8th numbers: 5 + 6 + 7 + 8 = 26Sum of the 1st four Mersenne numbers.Difference in the 2nd pair of amicable numbers = 1210 - 1184 = 26


27Can be partitioned 3010 ways.3x3x3The 3rd decagonal number.


28Can be partitioned 3718 ways.2x2x7The 4th hexagonal number.The 4th perfect number.


29Can be partitioned 4565 ways.The 10th prime number.


30Can be partitioned 5604 ways.2x3x5The 5th abundant number


31Can be partitioned 6842 ways.primeThe 5th mersenne number.The 3rd Mersenne prime number.The 5th centered triangular number.The 4th centered pentagonal number.


32Can be partitioned 8349 ways.2x2x2x2x2


33Can be partitioned 10143 ways.3x11


34Can be partitioned 12310 ways.2x17The 9th Fibonacci NumberThe 4th heptagonal number.


35Can be partitioned 14883 ways.5x7The 3rd centered cube number.


36Can be partitioned 17977 ways.2x2x3x3The 8th triangular number.The 6th Square Number.The 6th abundant number.


37Can be partitioned 21637ways.prime


38Can be partitioned ways.2x19The 2nd truncated octahedral number.


39Can be partitioned 26015 ways.3x13Product of the 2nd & 6th prime numbers= 3 x 13 = 39Sum of the 1st & 12th prime numbers = 2 + 37 = 39Sum of 10th odd & 10th even numbers = 19 + 20 = 39Sum of numbers 4 through 9 = 4 + 5 + 6 + 7 + 8 + 9 = 39Sum of the 6th, 7th, & 8th odd numbers = 11 + 13 + 15 = 39


40Can be partitioned 31185 ways.2x2x2x5The 4th octagonal number.Pentagonal Pyramidal NumberThe 7th abundant number


41Can be partitioned 37338 ways.primeThe 5th centered Square Number.


42Can be partitioned 44583 ways.2x3x7The 4th catalan number.The 8th abundant number.


43Can be partitioned 53174 ways.prime


44Can be partitioned 63261 ways.2x2x11The 4th octahedral number.


45Can be partitioned 75175 ways.Prime Divisors: 3x3x5The 5th hexagonal number.The 5th super catalan number


46Can be partitioned 89134 ways.Prime Divisors: 2x23The 4th nonagonal number.The 6th centered triangular number.


47Can be partitioned ways.Prime


48Can be partitioned ways.Prime Divisors: 2x2x2x2x3The 9th abundant number.


49Can be partitioned ways.Prime Divisors: 7x7


50Can be partitioned ways.2x5x5The 25th even number = 50Product of the 1st even & 13th odd numbers = 2 x 25 = 50Product of the 3rd odd & 5th even numbers = 5 x 10 = 50Sum of the 3rd cube and 9th prime numbers 27 + 23 = 50Sum of the 6th and 12th prime numbers 13 + 37 = 50Sum of the 8th and 11th prime numbers 19 + 31 = 50Sum of the 4th and 14th prime numbers 7 + 43 = 50Sum of the 1st three abundant numbers 12 + 18 + 20 = 50 sum of the squares of the Pythagorean 3-4-5 triangle= 9 + 16 + 25 = 50


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