248 (number)

248 (two hundred [and] forty-eight) is the natural number following 247 and preceding 249.

← 247 248 249 →
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Cardinaltwo hundred forty-eight
Ordinal248th
(two hundred forty-eighth)
Factorization23 × 31
Greek numeralΣΜΗ´
Roman numeralCCXLVIII
Binary111110002
Ternary1000123
Octal3708
Duodecimal18812
HexadecimalF816

In mathematics

248 is:

  • a nontotient.
  • a refactorable number.
  • an untouchable number.[1]
  • palindromic in bases 13 (16113), 30 (8830), 61 (4461), 123 (22123) and 247 (11247).
  • a Harshad number in bases 3, 4, 6, 7, 9, 11, 13 (and 18 other bases).
  • part of the 43-aliquot tree. The aliquot sequence starting at 248 is: 248, 232, 218, 112, 136, 134, 70, 74, 40, 50, 43, 1, 0.

The exceptional Lie group E8 has dimension 248.

In religion
  • The number 248 is the Gematria value for the Hebrew letters Ramach (Resh Mem and Het), traditionally depicted as the number of organs in the human body, and the number of positive commandments in the Torah. It is also the number of words in the Jewish Shema Prayer, inclusive of בָּרוּךְ שֵׁם כְּבוֹד מַלְכוּתוֹ לְעוֹלָם וָעֶד (Ba-ruch sheim k'vod mal-chu-to l'o-lam va-ed) in response to the first verse, and the repetition of יְהֹוָ֥ה אֱלֹֽהֵיכֶֽם אֱמֶ֔ת (A-do-nai E-lo-hei-chem Emet) by the Chazzan (prayer leader) in a Minyan (Quorum of ten Jews).

References
  1. Sloane, N. J. A. (ed.). "Sequence A005114 (Untouchable numbers: impossible values for sum of aliquot parts of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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