The number 81840

Q: Is 81840 a prime number?

No. 81840 = 2^4 × 3 × 5 × 11 × 31, so it is divisible by 2.

81840 is a composite number with 80 divisors. Its prime factorisation is $2^{4}$ × 3 × 5 × 11 × 31. Divisors (80): 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30 … 81840.

Number

Pick any whole number from 1 to 100,000.

81840 = 2^{4} \times 3 \times 5 \times 11 \times 31

Explain it step by step in chat Make a short video of it

How to work it out

1
81840 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
81840 is composite. Its prime factorisation is
$81840 = 2^{4} \times 3 \times 5 \times 11 \times 31$
3
The divisors add up to 285696; without 81840 itself that is 203856, so 81840 is abundant (203856 is more than 81840). Euler's totient φ(81840) = 19200 numbers up to 81840 share no factor with it.
4
The digits of 81840 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 63 steps to reach 1.

LaTeX source of the formulas on this page

\[ 81840 = 2^{4} \times 3 \times 5 \times 11 \times 31 \]

81840 at a glance

Property	Value
Type	composite
Number of divisors	80
Sum of divisors	285696
Euler totient φ(n)	19200
Square	6697785600
Cube	548146773504000
Square root	286.076913 (= 4√5115)
Digit sum / digital root	21 / 3
Collatz steps to 1	63
Scientific notation	8.184 × $10^{4}$

81840 in other forms

Form	Value
In words	eighty-one thousand eight hundred and forty
Binary (base 2)	10011111110110000
Octal (base 8)	237660
Hexadecimal (base 16)	13FB0
Base 3	11011021010
As time	81840 seconds = 22 h 44 min 0 s

Is 81840 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (81840 ÷ 2 = 40920)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (81840 ÷ 3 = 27280)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (81840 ÷ 4 = 20460)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (81840 ÷ 5 = 16368)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (81840 ÷ 6 = 13640)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 3)	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	Yes (81840 ÷ 8 = 10230)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 3)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (81840 ÷ 10 = 8184)	A number is divisible by 10 if the last digit is 0.
11	Yes (81840 ÷ 11 = 7440)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (81840 ÷ 12 = 6820)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 81840 a prime number?

No. 81840 = $2^{4}$ × 3 × 5 × 11 × 31, so it is divisible by 2.

What are the factors of 81840?

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 31, 33, 40, 44, 48, 55, 60, 62, 66, 80, 88, 93, 110, 120, 124, 132, 155, 165, 176, 186, 220, 240, 248, 264, 310, 330, 341, 372, 440, 465, 496, 528, 620, 660, 682, 744, 880, 930, 1023, 1240, 1320, 1364, 1488, 1705, 1860, 2046, 2480, 2640, 2728, 3410, 3720, 4092, 5115, 5456, 6820, 7440, 8184, 10230, 13640, 16368, 20460, 27280, 40920, 81840.

What is 81840 in binary?

10011111110110000 (hexadecimal 13FB0, octal 237660).

What is the square root of 81840?

About 286.0769, exactly 4√5115.

Is 81840 divisible by 3?

Yes. Its digits add up to 21, a multiple of 3.

What is special about the number 81840?

It is a composite number with 80 divisors.