The number 89880

Q: Is 89880 a prime number?

No. 89880 = 2^3 × 3 × 5 × 7 × 107, so it is divisible by 2.

89880 is a composite number with 64 divisors. Its prime factorisation is $2^{3}$ × 3 × 5 × 7 × 107. Divisors (64): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28 … 89880.

Number

Pick any whole number from 1 to 100,000.

89880 = 2^{3} \times 3 \times 5 \times 7 \times 107

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How to work it out

1
89880 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
89880 is composite. Its prime factorisation is
$89880 = 2^{3} \times 3 \times 5 \times 7 \times 107$
3
The divisors add up to 311040; without 89880 itself that is 221160, so 89880 is abundant (221160 is more than 89880). Euler's totient φ(89880) = 20352 numbers up to 89880 share no factor with it.
4
The digits of 89880 add up to 33, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 89 steps to reach 1.

LaTeX source of the formulas on this page

\[ 89880 = 2^{3} \times 3 \times 5 \times 7 \times 107 \]

89880 at a glance

Property	Value
Type	composite
Number of divisors	64
Sum of divisors	311040
Euler totient φ(n)	20352
Square	8078414400
Cube	726087886272000
Square root	299.799933 (= 2√22470)
Digit sum / digital root	33 / 6
Collatz steps to 1	89
Scientific notation	8.988 × $10^{4}$

89880 in other forms

Form	Value
In words	eighty-nine thousand eight hundred and eighty
Binary (base 2)	10101111100011000
Octal (base 8)	257430
Hexadecimal (base 16)	15F18
Base 3	11120021220
As time	89880 seconds = 24 h 58 min 0 s

Is 89880 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (89880 ÷ 2 = 44940)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (89880 ÷ 3 = 29960)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (89880 ÷ 4 = 22470)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (89880 ÷ 5 = 17976)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (89880 ÷ 6 = 14980)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (89880 ÷ 7 = 12840)	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 (89880 ÷ 8 = 11235)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 6)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (89880 ÷ 10 = 8988)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 10)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (89880 ÷ 12 = 7490)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 89880 a prime number?

No. 89880 = $2^{3}$ × 3 × 5 × 7 × 107, so it is divisible by 2.

What are the factors of 89880?

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 107, 120, 140, 168, 210, 214, 280, 321, 420, 428, 535, 642, 749, 840, 856, 1070, 1284, 1498, 1605, 2140, 2247, 2568, 2996, 3210, 3745, 4280, 4494, 5992, 6420, 7490, 8988, 11235, 12840, 14980, 17976, 22470, 29960, 44940, 89880.

What is 89880 in binary?

10101111100011000 (hexadecimal 15F18, octal 257430).

What is the square root of 89880?

About 299.7999, exactly 2√22470.

Is 89880 divisible by 3?

Yes. Its digits add up to 33, a multiple of 3.

What is special about the number 89880?

It is a composite number with 64 divisors.