The number 81180

Q: Is 81180 a prime number?

No. 81180 = 2^2 × 3^2 × 5 × 11 × 41, so it is divisible by 2.

81180 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × 5 × 11 × 41. Divisors (72): 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33 … 81180.

Number

Pick any whole number from 1 to 100,000.

81180 = 2^{2} \times 3^{2} \times 5 \times 11 \times 41

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How to work it out

1
What is special about 81180: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
2
81180 is composite. Its prime factorisation is
$81180 = 2^{2} \times 3^{2} \times 5 \times 11 \times 41$
3
The divisors add up to 275184; without 81180 itself that is 194004, so 81180 is abundant (194004 is more than 81180). Euler's totient φ(81180) = 19200 numbers up to 81180 share no factor with it.
4
The digits of 81180 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 76 steps to reach 1.

LaTeX source of the formulas on this page

\[ 81180 = 2^{2} \times 3^{2} \times 5 \times 11 \times 41 \]

81180 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	275184
Euler totient φ(n)	19200
Square	6590192400
Cube	534991819032000
Square root	284.921042 (= 6√2255)
Digit sum / digital root	18 / 9
Collatz steps to 1	76
Scientific notation	8.118 × $10^{4}$

81180 in other forms

Form	Value
In words	eighty-one thousand one hundred and eighty
Binary (base 2)	10011110100011100
Octal (base 8)	236434
Hexadecimal (base 16)	13D1C
Base 3	11010100200
As time	81180 seconds = 22 h 33 min 0 s

Is 81180 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (81180 ÷ 2 = 40590)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (81180 ÷ 3 = 27060)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (81180 ÷ 4 = 20295)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (81180 ÷ 5 = 16236)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (81180 ÷ 6 = 13530)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 1)	A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7.
8	No (remainder 4)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (81180 ÷ 9 = 9020)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (81180 ÷ 10 = 8118)	A number is divisible by 10 if the last digit is 0.
11	Yes (81180 ÷ 11 = 7380)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (81180 ÷ 12 = 6765)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 81180 a prime number?

No. 81180 = $2^{2}$ × $3^{2}$ × 5 × 11 × 41, so it is divisible by 2.

What are the factors of 81180?

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 41, 44, 45, 55, 60, 66, 82, 90, 99, 110, 123, 132, 164, 165, 180, 198, 205, 220, 246, 330, 369, 396, 410, 451, 492, 495, 615, 660, 738, 820, 902, 990, 1230, 1353, 1476, 1804, 1845, 1980, 2255, 2460, 2706, 3690, 4059, 4510, 5412, 6765, 7380, 8118, 9020, 13530, 16236, 20295, 27060, 40590, 81180.

What is 81180 in binary?

10011110100011100 (hexadecimal 13D1C, octal 236434).

What is the square root of 81180?

About 284.9210, exactly 6√2255.

Is 81180 divisible by 3?

Yes. Its digits add up to 18, a multiple of 3.

What is special about the number 81180?

81180 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.