# Properties of Number

Click on number to see Concepts connected with it.0 |

Can be partitioned 1 way. |

n/a |

1 |

Can be partitioned 1 way. |

n/a |

2 |

Can be partitioned 2 ways. |

Prime |

The 3th Fibonacci Number. |

The 1st Mersenne prime number. |

3 |

Can be partitioned 3 ways. |

Prime |

The 2nd mersenne number. |

triangular number |

The 4th Fibonacci Number. |

The 1st Delannoy Number. |

4 |

Can be partitioned 5 ways. |

2x2 |

Square Number |

5 |

Can be partitioned 7 ways. |

Prime |

The 8th Fibonacci Number. |

The 3rd catalan number. |

6 |

Can be partitioned 11 ways. |

2x3 |

The 3rd triangular number. |

The 2nd hexagonal number. |

The 2nd Schröder number. |

7 |

Can 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 = 7 |

Difference of the first two cube numbers = 23 - 13 = 8 - 1 = 7 |

Sum of the 2nd odd & 2nd even numbers = 3 + 4 = 7 |

Sum of the 1st & 3rd prime numbers= 2 + 5 = 7 |

Sum of the 1st & 3rd factorials= 1 + 6 = 7 |

Sum of the 1st & 3rd triangular numbers= 1 + 6 = 7 |

8 |

Can be partitioned 22 ways. |

2x2x2 |

The 5th Fibonacci Number. |

9 |

Can be partitioned 30 ways. |

3x3 |

The 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 = 9 |

Sum of the first three odd numbers. |

Sum of the first three factorials= 1 + 2 + 6 = 9 |

10 |

Can be partitioned 42 ways. |

2x5 |

The 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 = 10 |

Product of the 1st & 3rd prime numbers= 2 x 5 = 10 |

Product of the 3rd & 5th Fibonacci numbers= 2 x 5 = 10 |

Sum of the 1st three prime numbers = 2 + 3 + 5 = 10 |

Sum of the 3rd, 4th, 5th Fibonacci numbers= 2 + 3 + 5 = 10 |

Sum of the 1st & 3rd Square Numbers= 12 + 32 = 1 + 9 = 10 |

Sum of the 1st & 4th even numbers = 2 + 8 = 10 |

Sum of the 2nd & 4th odd numbers = 3 + 7 = 10 |

Sum of the 2nd & 3rd,(2n - 1): 3 + 7 = 10 |

Sum of the 2nd & 3rd even numbers = 4 + 6 = 10 |

11 |

Can be partitioned 56 ways. |

Prime |

The 4th super catalan number |

12 |

Can be partitioned 77 ways. |

2x2x3 |

The 1st abundant number |

13 |

Can 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 = 13 |

Sum of the 1st perfect number & 4th prime number= 6 + 7 = 13 |

The hypotenuse of the Pythagorean 5-12-13 triangle= 13 |

14 |

Can be partitioned 135 ways. |

2x7 |

The 7th even number. |

The 7th composite number. |

The 4th catalan number. |

The 3rd pyramidal number = 1, 5, 14 |

Product of the 1st even & 4th odd numbers = 2 x 7 = 14 |

Sum of the 1st, 2nd, & 4th triangular numbers= 1 + 3 + 10 = 14 |

Sum of the 1st, 3rd, and 4th prime numbers= 2 + 5 + 7 = 14 |

Sum of the 1st and 7th Fibonacci numbers= 1 + 13 = 14 |

Sum of the 1st & 6th even numbers = 2 + 12 = 14 |

Sum of the 2nd & 5th even numbers = 4 + 10 = 14 |

Sum of the 3rd & 4th even numbers = 6 + 8 = 14 |

Sum of the 2nd, 3rd, 4th, 5th numbers = 2 + 3 + 4 + 5 = 14 |

15 |

Can be partitioned 176 ways. |

3x5 |

The 5th triangular number. |

The 3rd hexagonal number. |

The 4th mersenne number. |

16 |

Can be partitioned 231 ways. |

2x2x2x2 |

Square Number |

The 3rd centered pentagonal number. |

The 2nd truncated tetrahedal number. |

17 |

Can be partitioned 297 ways. |

Prime |

18 |

Can be partitioned 385 ways. |

2x3x3 |

Pentagonal Pyramidal Number |

The 3rd heptagonal number. |

The 2nd abundant number |

19 |

Can be partitioned 490 ways. |

Prime |

The 4th centered triangular number. |

The 3rd octahedral number. |

20 |

Can be partitioned 627 ways. |

2x2x5 |

The 1st abundant number. |

21 |

Can be partitioned 792 ways. |

3x7 |

triangular number |

The 3rd octagonal number. |

The 8th Fibonacci Number. |

22 |

Can be partitioned 1002 ways. |

2x11 |

Twenty-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. |

23 |

Can 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. |

24 |

Can be partitioned 1575 ways. |

2x2x2x3 |

The 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, 24 |

Product of the 1st and 6th even numbers = 2 x 12 = 24 |

Product of the 2nd and 3rd even numbers = 4 x 6 = 24 |

Product of the 1st composite & 1st perfect number 4 x 6 = 24 |

Product of the 2nd triangular & 2nd cube numbers = 3 x 8 = 24 |

Sum of the 5th and 6th prime numbers 11 + 13 = 24 |

The 4th abundant number= 12, 18, 20, 24 |

Factorial 4 = 4! = 4 x 3 x 2 x 1 = 24 |

25 |

Can be partitioned 1958 ways. |

5x5 |

The 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) |

26 |

Can be partitioned 2436 ways. |

2x13 |

The 13th even number. |

The 3rd heptagonal pyramidal number. |

Product of the 1st even and 7th odd numbers = 2 x 13 = 26 |

Sum of the 1st & 5th Square Numbers = 12 + 52 = 1 + 25 = 26 |

Sum of the 6th & 7th even numbers = 12 + 14 = 26 |

Sum of the 5th, 6th, and 7th Fibonacci numbers = 5 + 8 + 13 = 26 |

Sum of the 5th through 8th numbers: 5 + 6 + 7 + 8 = 26 |

Sum of the 1st four Mersenne numbers. |

Difference in the 2nd pair of amicable numbers = 1210 - 1184 = 26 |

27 |

Can be partitioned 3010 ways. |

3x3x3 |

The 3rd decagonal number. |

28 |

Can be partitioned 3718 ways. |

2x2x7 |

The 4th hexagonal number. |

The 4th perfect number. |

29 |

Can be partitioned 4565 ways. |

The 10th prime number. |

30 |

Can be partitioned 5604 ways. |

2x3x5 |

The 5th abundant number |

31 |

Can be partitioned 6842 ways. |

prime |

The 5th mersenne number. |

The 3rd Mersenne prime number. |

The 5th centered triangular number. |

The 4th centered pentagonal number. |

32 |

Can be partitioned 8349 ways. |

2x2x2x2x2 |

33 |

Can be partitioned 10143 ways. |

3x11 |

34 |

Can be partitioned 12310 ways. |

2x17 |

The 9th Fibonacci Number |

The 4th heptagonal number. |

35 |

Can be partitioned 14883 ways. |

5x7 |

The 3rd centered cube number. |

36 |

Can be partitioned 17977 ways. |

2x2x3x3 |

The 8th triangular number. |

The 6th Square Number. |

The 6th abundant number. |

37 |

Can be partitioned 21637ways. |

prime |

38 |

Can be partitioned ways. |

2x19 |

The 2nd truncated octahedral number. |

39 |

Can be partitioned 26015 ways. |

3x13 |

Product of the 2nd & 6th prime numbers= 3 x 13 = 39 |

Sum of the 1st & 12th prime numbers = 2 + 37 = 39 |

Sum of 10th odd & 10th even numbers = 19 + 20 = 39 |

Sum of numbers 4 through 9 = 4 + 5 + 6 + 7 + 8 + 9 = 39 |

Sum of the 6th, 7th, & 8th odd numbers = 11 + 13 + 15 = 39 |

40 |

Can be partitioned 31185 ways. |

2x2x2x5 |

The 4th octagonal number. |

Pentagonal Pyramidal Number |

The 7th abundant number |

41 |

Can be partitioned 37338 ways. |

prime |

The 5th centered Square Number. |

42 |

Can be partitioned 44583 ways. |

2x3x7 |

The 4th catalan number. |

The 8th abundant number. |

43 |

Can be partitioned 53174 ways. |

prime |

44 |

Can be partitioned 63261 ways. |

2x2x11 |

The 4th octahedral number. |

45 |

Can be partitioned 75175 ways. |

Prime Divisors: 3x3x5 |

The 5th hexagonal number. |

The 5th super catalan number |

46 |

Can be partitioned 89134 ways. |

Prime Divisors: 2x23 |

The 4th nonagonal number. |

The 6th centered triangular number. |

47 |

Can be partitioned ways. |

Prime |

48 |

Can be partitioned ways. |

Prime Divisors: 2x2x2x2x3 |

The 9th abundant number. |

49 |

Can be partitioned ways. |

Prime Divisors: 7x7 |

50 |

Can be partitioned ways. |

2x5x5 |

The 25th even number = 50 |

Product of the 1st even & 13th odd numbers = 2 x 25 = 50 |

Product of the 3rd odd & 5th even numbers = 5 x 10 = 50 |

Sum of the 3rd cube and 9th prime numbers 27 + 23 = 50 |

Sum of the 6th and 12th prime numbers 13 + 37 = 50 |

Sum of the 8th and 11th prime numbers 19 + 31 = 50 |

Sum of the 4th and 14th prime numbers 7 + 43 = 50 |

Sum 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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