The number 81600

Q: Is 81600 a prime number?

No. 81600 = 2^6 × 3 × 5^2 × 17, so it is divisible by 2.

81600 is a composite number with 84 divisors. Its prime factorisation is $2^{6}$ × 3 × $5^{2}$ × 17. Divisors (84): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 25, 30 … 81600.

Number

Pick any whole number from 1 to 100,000.

81600 = 2^{6} \times 3 \times 5^{2} \times 17

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How to work it out

1
What is special about 81600: a Harshad number: divisible by its digit sum 15.
2
81600 is composite. Its prime factorisation is
$81600 = 2^{6} \times 3 \times 5^{2} \times 17$
3
The divisors add up to 283464; without 81600 itself that is 201864, so 81600 is abundant (201864 is more than 81600). Euler's totient φ(81600) = 20480 numbers up to 81600 share no factor with it.
4
The digits of 81600 add up to 15, 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

\[ 81600 = 2^{6} \times 3 \times 5^{2} \times 17 \]

81600 at a glance

Property	Value
Type	composite
Number of divisors	84
Sum of divisors	283464
Euler totient φ(n)	20480
Square	6658560000
Cube	543338496000000
Square root	285.657137 (= 40√51)
Digit sum / digital root	15 / 6
Collatz steps to 1	89
Scientific notation	8.16 × $10^{4}$

81600 in other forms

Form	Value
In words	eighty-one thousand six hundred
Binary (base 2)	10011111011000000
Octal (base 8)	237300
Hexadecimal (base 16)	13EC0
Base 3	11010221020
As time	81600 seconds = 22 h 40 min 0 s

Is 81600 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (81600 ÷ 2 = 40800)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (81600 ÷ 3 = 27200)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (81600 ÷ 4 = 20400)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (81600 ÷ 5 = 16320)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (81600 ÷ 6 = 13600)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 1)	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 (81600 ÷ 8 = 10200)	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 (81600 ÷ 10 = 8160)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 2)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (81600 ÷ 12 = 6800)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 81600 a prime number?

No. 81600 = $2^{6}$ × 3 × $5^{2}$ × 17, so it is divisible by 2.

What are the factors of 81600?

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 25, 30, 32, 34, 40, 48, 50, 51, 60, 64, 68, 75, 80, 85, 96, 100, 102, 120, 136, 150, 160, 170, 192, 200, 204, 240, 255, 272, 300, 320, 340, 400, 408, 425, 480, 510, 544, 600, 680, 800, 816, 850, 960, 1020, 1088, 1200, 1275, 1360, 1600, 1632, 1700, 2040, 2400, 2550, 2720, 3264, 3400, 4080, 4800, 5100, 5440, 6800, 8160, 10200, 13600, 16320, 20400, 27200, 40800, 81600.

What is 81600 in binary?

10011111011000000 (hexadecimal 13EC0, octal 237300).

What is the square root of 81600?

About 285.6571, exactly 40√51.

Is 81600 divisible by 3?

Yes. Its digits add up to 15, a multiple of 3.

What is special about the number 81600?

81600 is a Harshad number: divisible by its digit sum 15.