170 (number)
Encyclopedia
170 is the natural number following 169
and preceding 171
.
. Nor is it ever a solution to x - φ(x), making it a noncototient
.
The proper divisors of 170 are 1, 2, 5, 10
, 17
, 34
, and 85
. These add up to 154
, which is less than 170, and thus 170 is a deficient number
.
Written as 2222 in base 4
, 170 is a repdigit
.
170 is the largest integer for which Google
's built-in calculator
function can compute the factorial
, returning the answer as 170! = 7.25741562 × 10306.
169 (number)
169 is the natural number following 168 and preceding 170.-In mathematics:* 169 is an odd number* 169 is a square number. 13 x 13 = 169, and the reverse 31 x 31 = 961...
and preceding 171
171 (number)
171 is the natural number following 170 and preceding 172.-In mathematics:* 171 is an odd number* 171 is a composite number* 171 is a deficient number* 171 is a Harshad number, divisible by the sum of its digits...
.
| Cardinal Cardinal number In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a finite set is a natural number – the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite... | One hundred [and] seventy |
| Ordinal Ordinal number In set theory, an ordinal number, or just ordinal, is the order type of a well-ordered set. They are usually identified with hereditarily transitive sets. Ordinals are an extension of the natural numbers different from integers and from cardinals... |
170th |
| Factorization Factorization In mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original... |  |
| Divisors | 1, 2, 5, 10, 17, 34, 85, 170 |
| Roman numeral | CLXX |
| Binary Binary numeral system The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2... |
10101010 |
| Hexadecimal Hexadecimal In mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen... |
AA |
In mathematics
170 is the smallest n for which φ(n) and σ(n) are both square(64 and 324 respectively). But 170 is never a solution for φ(x), making it a nontotientNontotient
In number theory, a nontotient is a positive integer n which is not in the range of Euler's totient function φ, that is, for which φ = n has no solution. In other words, n is a nontotient if there is no integer x that has exactly n coprimes below it. All odd numbers are nontotients, except 1,...
. Nor is it ever a solution to x - φ(x), making it a noncototient
Noncototient
In mathematics, a noncototient is a positive integer n that cannot be expressed as the difference between a positive integer m and the number of coprime integers below it. That is, m − φ = n, where φ stands for Euler's totient function, has no solution for m...
.
The proper divisors of 170 are 1, 2, 5, 10
10 (number)
10 is an even natural number following 9 and preceding 11.-In mathematics:Ten is a composite number, its proper divisors being , and...
, 17
17 (number)
17 is the natural number following 16 and preceding 18. It is prime.In spoken English, the numbers 17 and 70 are sometimes confused because they sound similar. When carefully enunciated, they differ in which syllable is stressed: 17 vs 70...
, 34
34 (number)
34 is the natural number following 33 and preceding 35.-In mathematics:34 is the ninth distinct semiprime and has four divisors including unity and itself. Its neighbors, 33 and 35, also are distinct semiprimes, having four divisors each, and 34 is the smallest number to be surrounded by numbers...
, and 85
85 (number)
85 is the natural number following 84 and preceding 86.-In mathematics:85 is an octahedral number, a centered triangular number, a centered square number, a decagonal number, and a Smith number....
. These add up to 154
154 (number)
One hundred and fifty-four is the natural number following one hundred and fifty-three and preceding one hundred and fifty-five.-In mathematics:* 154 is a nonagonal number...
, which is less than 170, and thus 170 is a deficient number
Deficient number
In number theory, a deficient number or defective number is a number n for which the sum of divisors σIn number theory, a deficient number or defective number is a number n for which the sum of divisors σIn number theory, a deficient number or defective number is a number n for which...
.
Written as 2222 in base 4
Quaternary numeral system
Quaternary is the base- numeral system. It uses the digits 0, 1, 2 and 3 to represent any real number.It shares with all fixed-radix numeral systems many properties, such as the ability to represent any real number with a canonical representation and the characteristics of the representations of...
, 170 is a repdigit
Repdigit
In recreational mathematics, a repdigit is a natural number composed of repeated instances of the same digit, most often in the decimal numeral system....
.
170 is the largest integer for which Google
Google
Google Inc. is an American multinational public corporation invested in Internet search, cloud computing, and advertising technologies. Google hosts and develops a number of Internet-based services and products, and generates profit primarily from advertising through its AdWords program...
's built-in calculator
Calculator
An electronic calculator is a small, portable, usually inexpensive electronic device used to perform the basic operations of arithmetic. Modern calculators are more portable than most computers, though most PDAs are comparable in size to handheld calculators.The first solid-state electronic...
function can compute the factorial
Factorial
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n...
, returning the answer as 170! = 7.25741562 × 10306.
In sports
- 170 is the maximum check-out possible in a standard game of dartsDartsDarts is a form of throwing game where darts are thrown at a circular target fixed to a wall. Though various boards and games have been used in the past, the term "darts" usually now refers to a standardised game involving a specific board design and set of rules...
(where the final score must be a double). It consists of two treble-twenties and a double-bullseye.
See also
- 170s170s-Significant people:* Marcus Aurelius, Roman Emperor* Caerellius Priscus, governor of Roman Britain...
- E170 (disambiguation)
- F170 (disambiguation)
- List of highways numbered 170
- United States Supreme Court cases, Volume 170
- United Nations Security Council Resolution 170United Nations Security Council Resolution 170United Nations Security Council Resolution 170, adopted unanimously on December 14, 1961, examined the application of Tanganyika for membership in the United Nations. The Council recommended to the General Assembly that Tanganyika be admitted.-References:...
- Pennsylvania House of Representatives, District 170Pennsylvania House of Representatives, District 170The 170th Pennsylvania House of Representatives District is made up of parts of Montgomery County and Philadelphia County. The shape of the district makes it a prime example of gerrymandering...
- 170th meridian west170th meridian westThe meridian 170° west of Greenwich is a line of longitude that extends from the North Pole across the Arctic Ocean, Asia, the Pacific Ocean, the Southern Ocean, and Antarctica to the South Pole....
and 170th meridian east170th meridian eastThe meridian 170° east of Greenwich is a line of longitude that extends from the North Pole across the Arctic Ocean, Asia, the Pacific Ocean, New Zealand, the Southern Ocean, and Antarctica to the South Pole....