The number 83880

Q: Is 83880 a prime number?

No. 83880 = 2^3 × 3^2 × 5 × 233, so it is divisible by 2.

83880 is a composite number with 48 divisors. Its prime factorisation is $2^{3}$ × $3^{2}$ × 5 × 233. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36 … 83880.

Number

Pick any whole number from 1 to 100,000.

83880 = 2^{3} \times 3^{2} \times 5 \times 233

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How to work it out

1
83880 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
83880 is composite. Its prime factorisation is
$83880 = 2^{3} \times 3^{2} \times 5 \times 233$
3
The divisors add up to 273780; without 83880 itself that is 189900, so 83880 is abundant (189900 is more than 83880). Euler's totient φ(83880) = 22272 numbers up to 83880 share no factor with it.
4
The digits of 83880 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 151 steps to reach 1.

LaTeX source of the formulas on this page

\[ 83880 = 2^{3} \times 3^{2} \times 5 \times 233 \]

83880 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	273780
Euler totient φ(n)	22272
Square	7035854400
Cube	590167467072000
Square root	289.620441 (= 6√2330)
Digit sum / digital root	27 / 9
Collatz steps to 1	151
Scientific notation	8.388 × $10^{4}$

83880 in other forms

Form	Value
In words	eighty-three thousand eight hundred and eighty
Binary (base 2)	10100011110101000
Octal (base 8)	243650
Hexadecimal (base 16)	147A8
Base 3	11021001200
As time	83880 seconds = 23 h 18 min 0 s

Is 83880 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (83880 ÷ 2 = 41940)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (83880 ÷ 3 = 27960)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (83880 ÷ 4 = 20970)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (83880 ÷ 5 = 16776)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (83880 ÷ 6 = 13980)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 6)	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 (83880 ÷ 8 = 10485)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (83880 ÷ 9 = 9320)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (83880 ÷ 10 = 8388)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 5)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (83880 ÷ 12 = 6990)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 83880 a prime number?

No. 83880 = $2^{3}$ × $3^{2}$ × 5 × 233, so it is divisible by 2.

What are the factors of 83880?

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 233, 360, 466, 699, 932, 1165, 1398, 1864, 2097, 2330, 2796, 3495, 4194, 4660, 5592, 6990, 8388, 9320, 10485, 13980, 16776, 20970, 27960, 41940, 83880.

What is 83880 in binary?

10100011110101000 (hexadecimal 147A8, octal 243650).

What is the square root of 83880?

About 289.6204, exactly 6√2330.

Is 83880 divisible by 3?

Yes. Its digits add up to 27, a multiple of 3.

What is special about the number 83880?

It is a composite number with 48 divisors.