The number 88920

Q: Is 88920 a prime number?

No. 88920 = 2^3 × 3^2 × 5 × 13 × 19, so it is divisible by 2.

88920 is a composite number with 96 divisors. Its prime factorisation is $2^{3}$ × $3^{2}$ × 5 × 13 × 19. Divisors (96): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 18, 19, 20, 24 … 88920.

Number

Pick any whole number from 1 to 100,000.

88920 = 2^{3} \times 3^{2} \times 5 \times 13 \times 19

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

How to work it out

1
88920 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
88920 is composite. Its prime factorisation is
$88920 = 2^{3} \times 3^{2} \times 5 \times 13 \times 19$
3
The divisors add up to 327600; without 88920 itself that is 238680, so 88920 is abundant (238680 is more than 88920). Euler's totient φ(88920) = 20736 numbers up to 88920 share no factor with it.
4
The digits of 88920 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 164 steps to reach 1.

LaTeX source of the formulas on this page

\[ 88920 = 2^{3} \times 3^{2} \times 5 \times 13 \times 19 \]

88920 at a glance

Property	Value
Type	composite
Number of divisors	96
Sum of divisors	327600
Euler totient φ(n)	20736
Square	7906766400
Cube	703069668288000
Square root	298.194567 (= 6√2470)
Digit sum / digital root	27 / 9
Collatz steps to 1	164
Scientific notation	8.892 × $10^{4}$

88920 in other forms

Form	Value
In words	eighty-eight thousand nine hundred and twenty
Binary (base 2)	10101101101011000
Octal (base 8)	255530
Hexadecimal (base 16)	15B58
Base 3	11111222100
As time	88920 seconds = 24 h 42 min 0 s

Is 88920 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (88920 ÷ 2 = 44460)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (88920 ÷ 3 = 29640)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (88920 ÷ 4 = 22230)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (88920 ÷ 5 = 17784)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (88920 ÷ 6 = 14820)	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 (88920 ÷ 8 = 11115)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (88920 ÷ 9 = 9880)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (88920 ÷ 10 = 8892)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 7)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (88920 ÷ 12 = 7410)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 88920 a prime number?

No. 88920 = $2^{3}$ × $3^{2}$ × 5 × 13 × 19, so it is divisible by 2.

What are the factors of 88920?

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 18, 19, 20, 24, 26, 30, 36, 38, 39, 40, 45, 52, 57, 60, 65, 72, 76, 78, 90, 95, 104, 114, 117, 120, 130, 152, 156, 171, 180, 190, 195, 228, 234, 247, 260, 285, 312, 342, 360, 380, 390, 456, 468, 494, 520, 570, 585, 684, 741, 760, 780, 855, 936, 988, 1140, 1170, 1235, 1368, 1482, 1560, 1710, 1976, 2223, 2280, 2340, 2470, 2964, 3420, 3705, 4446, 4680, 4940, 5928, 6840, 7410, 8892, 9880, 11115, 14820, 17784, 22230, 29640, 44460, 88920.

What is 88920 in binary?

10101101101011000 (hexadecimal 15B58, octal 255530).

What is the square root of 88920?

About 298.1946, exactly 6√2470.

Is 88920 divisible by 3?

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

What is special about the number 88920?

It is a composite number with 96 divisors.