248 (number)

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

← 247 248 249 →
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Cardinal	two hundred forty-eight
Ordinal	248th (two hundred forty-eighth)
Factorization	2^3 × 31
Greek numeral	ΣΜΗ´
Roman numeral	CCXLVIII
Binary	111110002
Ternary	1000123
Octal	3708
Duodecimal	18812
Hexadecimal	F816

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.