6174

← 6173 6174 6175 →
List of numbers Integers ← 0 1k 2k 3k 4k 5k 6k 7k 8k 9k →
Cardinal	six thousand one hundred seventy-four
Ordinal	6174th (six thousand one hundred seventy-fourth)
Factorization	2 × 32 × 73
Divisors	1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 343, 441, 686, 882, 1029, 2058, 3087, 6174
Greek numeral	,ϚΡΟΔ´
Roman numeral	VMCLXXIV, or VICLXXIV
Binary	11000000111102
Ternary	221102003
Senary	443306
Octal	140368
Duodecimal	36A612
Hexadecimal	181E16

6174 (six thousand, one hundred [and] seventy-four) is the natural number following 6173 and preceding 6175.

Properties

• It is a Kaprekar's Constant
• 6174 is a 7-smooth number, i.e., none of its prime factors is greater than 7.
• 6174 can be written as the sum of the first three powers of 18:
  • 18³ + 18² + 18¹ = 5832 + 324 + 18 = 6174, and coincidentally, 6 + 1 + 7 + 4 = 18.
• The sum of squares of the prime factors of 6174 is a square:
  • 2² + 3² + 3² + 7² + 7² + 7² = 4 + 9 + 9 + 49 + 49 + 49 = 169 = 13²

External links

• Bowley, Roger (5 December 2011). "6174 is Kaprekar's Constant". Numberphile. University of Nottingham: Brady Haran.
• Sample (Perl) code to walk any four-digit number to Kaprekar’s Constant
• Sample (Python) code to walk any four-digit number to Kaprekar’s Constant
• Sample (C) code to walk the first 10000 numbers and their steps to Kaprekar’s Constant