The number 86112

Q: Is 86112 a prime number?

No. 86112 = 2^5 × 3^2 × 13 × 23, so it is divisible by 2.

86112 is a composite number with 72 divisors. Its prime factorisation is $2^{5}$ × $3^{2}$ × 13 × 23. Divisors (72): 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 23, 24, 26, 32, 36 … 86112.

Number

Pick any whole number from 1 to 100,000.

86112 = 2^{5} \times 3^{2} \times 13 \times 23

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How to work it out

1
What is special about 86112: a Harshad number: divisible by its digit sum 18.
2
86112 is composite. Its prime factorisation is
$86112 = 2^{5} \times 3^{2} \times 13 \times 23$
3
The divisors add up to 275184; without 86112 itself that is 189072, so 86112 is abundant (189072 is more than 86112). Euler's totient φ(86112) = 25344 numbers up to 86112 share no factor with it.
4
The digits of 86112 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 120 steps to reach 1.

LaTeX source of the formulas on this page

\[ 86112 = 2^{5} \times 3^{2} \times 13 \times 23 \]

86112 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	275184
Euler totient φ(n)	25344
Square	7415276544
Cube	638544293756928
Square root	293.448462 (= 12√598)
Digit sum / digital root	18 / 9
Collatz steps to 1	120
Scientific notation	8.6112 × $10^{4}$

86112 in other forms

Form	Value
In words	eighty-six thousand one hundred and twelve
Binary (base 2)	10101000001100000
Octal (base 8)	250140
Hexadecimal (base 16)	15060
Base 3	11101010100
As time	86112 seconds = 23 h 55 min 12 s

Is 86112 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (86112 ÷ 2 = 43056)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (86112 ÷ 3 = 28704)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (86112 ÷ 4 = 21528)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 2)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (86112 ÷ 6 = 14352)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 5)	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 (86112 ÷ 8 = 10764)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (86112 ÷ 9 = 9568)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 2)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 4)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (86112 ÷ 12 = 7176)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 86112 a prime number?

No. 86112 = $2^{5}$ × $3^{2}$ × 13 × 23, so it is divisible by 2.

What are the factors of 86112?

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 23, 24, 26, 32, 36, 39, 46, 48, 52, 69, 72, 78, 92, 96, 104, 117, 138, 144, 156, 184, 207, 208, 234, 276, 288, 299, 312, 368, 414, 416, 468, 552, 598, 624, 736, 828, 897, 936, 1104, 1196, 1248, 1656, 1794, 1872, 2208, 2392, 2691, 3312, 3588, 3744, 4784, 5382, 6624, 7176, 9568, 10764, 14352, 21528, 28704, 43056, 86112.

What is 86112 in binary?

10101000001100000 (hexadecimal 15060, octal 250140).

What is the square root of 86112?

About 293.4485, exactly 12√598.

Is 86112 divisible by 3?

Yes. Its digits add up to 18, a multiple of 3.

What is special about the number 86112?

86112 is a Harshad number: divisible by its digit sum 18.