The number 87880

Q: Is 87880 a prime number?

No. 87880 = 2^3 × 5 × 13^3, so it is divisible by 2.

87880 is a composite number with 32 divisors. Its prime factorisation is $2^{3}$ × 5 × $13^{3}$ . Divisors (32): 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 169, 260 … 87880.

Number

Pick any whole number from 1 to 100,000.

87880 = 2^{3} \times 5 \times 13^{3}

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How to work it out

1
87880 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
87880 is composite. Its prime factorisation is
$87880 = 2^{3} \times 5 \times 13^{3}$
3
The divisors add up to 214200; without 87880 itself that is 126320, so 87880 is abundant (126320 is more than 87880). Euler's totient φ(87880) = 32448 numbers up to 87880 share no factor with it.
4
The digits of 87880 add up to 31, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 164 steps to reach 1.

LaTeX source of the formulas on this page

\[ 87880 = 2^{3} \times 5 \times 13^{3} \]

87880 at a glance

Property	Value
Type	composite
Number of divisors	32
Sum of divisors	214200
Euler totient φ(n)	32448
Square	7722894400
Cube	678687959872000
Square root	296.445611 (= 26√130)
Digit sum / digital root	31 / 4
Collatz steps to 1	164
Scientific notation	8.788 × $10^{4}$

87880 in other forms

Form	Value
In words	eighty-seven thousand eight hundred and eighty
Binary (base 2)	10101011101001000
Octal (base 8)	253510
Hexadecimal (base 16)	15748
Base 3	11110112211
As time	87880 seconds = 24 h 24 min 40 s

Is 87880 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (87880 ÷ 2 = 43940)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	No (remainder 1)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (87880 ÷ 4 = 21970)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (87880 ÷ 5 = 17576)	A number is divisible by 5 if the last digit is 0 or 5.
6	No (remainder 4)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 2)	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 (87880 ÷ 8 = 10985)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 4)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (87880 ÷ 10 = 8788)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 1)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	No (remainder 4)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 87880 a prime number?

No. 87880 = $2^{3}$ × 5 × $13^{3}$ , so it is divisible by 2.

What are the factors of 87880?

1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 169, 260, 338, 520, 676, 845, 1352, 1690, 2197, 3380, 4394, 6760, 8788, 10985, 17576, 21970, 43940, 87880.

What is 87880 in binary?

10101011101001000 (hexadecimal 15748, octal 253510).

What is the square root of 87880?

About 296.4456, exactly 26√130.

Is 87880 divisible by 3?

No. Its digits add up to 31, which is not a multiple of 3.

What is special about the number 87880?

It is a composite number with 32 divisors.