213 (number)

Last updated
212 213 214
Cardinal two hundred thirteen
Ordinal 213th
(two hundred thirteenth)
Factorization 3 × 71
Divisors 1, 3, 71, 213
Greek numeral ΣΙΓ´
Roman numeral CCXIII
Binary 110101012
Ternary 212203
Senary 5536
Octal 3258
Duodecimal 15912
Hexadecimal D516

213 (two hundred [and] thirteen) is the number following 212 and preceding 214.

Contents

In mathematics

213 and the other permutations of its digits are the only three-digit number whose digit sums and digit products are equal. [1] It is a member of the quickly-growing Levine sequence, constructed from a triangle of numbers in which each row counts the copies of each value in the row below it. [2] [3]

As the product of the two distinct prime numbers 3 and 71, it is a semiprime, the first of a triple of three consecutive semiprimes 213, 214, and 215. [4] Its square, 2132 = 45369, is one of only 15 known squares that can be represented as a sum of distinct factorials. [5]

See also

Related Research Articles

2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultures.

In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. Because there are infinitely many prime numbers, there are also infinitely many semiprimes. Semiprimes are also called biprimes.

38 (thirty-eight) is the natural number following 37 and preceding 39.

69 (sixty-nine) is the natural number following 68 and preceding 70.

35 (thirty-five) is the natural number following 34 and preceding 36.

86 (eighty-six) is the natural number following 85 and preceding 87.

39 (thirty-nine) is the natural number following 38 and preceding 40.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

300 is the natural number following 299 and preceding 301.

400 is the natural number following 399 and preceding 401.

700 is the natural number following 699 and preceding 701.

600 is the natural number following 599 and preceding 601.

800 is the natural number following 799 and preceding 801.

135 is the natural number following 134 and preceding 136.

<span class="mw-page-title-main">1,000,000</span> Natural number

One million (1,000,000), or one thousand thousand, is the natural number following 999,999 and preceding 1,000,001. The word is derived from the early Italian millione, from mille, "thousand", plus the augmentative suffix -one.

100,000 (one hundred thousand) is the natural number following 99,999 and preceding 100,001. In scientific notation, it is written as 105.

216 is the natural number following 215 and preceding 217. It is a cube, and is often called Plato's number, although it is not certain that this is the number intended by Plato.

10,000,000 is the natural number following 9,999,999 and preceding 10,000,001.

209 is the natural number following 208 and preceding 210.

744 is the natural number following 743 and preceding 745.

References

  1. Sloane, N. J. A. (ed.). "SequenceA034710(Positive numbers for which the sum of digits equals the product of digits)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. Sloane, N. J. A. (ed.). "SequenceA011784(Levine's sequence)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  3. Guy, Richard K. (April 1998). "What's left?". Math Horizons. 5 (4): 5–7. doi:10.1080/10724117.1998.11975052. JSTOR   25678158.
  4. Sloane, N. J. A. (ed.). "SequenceA039833(Smallest of three consecutive squarefree numbers k, k+1, k+2 of the form p*q where p and q are primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  5. Sloane, N. J. A. (ed.). "SequenceA014597(Numbers k such that k^2 is a sum of distinct factorials)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.