The number 82320

Q: Is 82320 a prime number?

No. 82320 = 2^4 × 3 × 5 × 7^3, so it is divisible by 2.

82320 is a composite number with 80 divisors. Its prime factorisation is $2^{4}$ × 3 × 5 × $7^{3}$ . Divisors (80): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24 … 82320.

Number

Pick any whole number from 1 to 100,000.

82320 = 2^{4} \times 3 \times 5 \times 7^{3}

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How to work it out

1
What is special about 82320: a Harshad number: divisible by its digit sum 15.
2
82320 is composite. Its prime factorisation is
$82320 = 2^{4} \times 3 \times 5 \times 7^{3}$
3
The divisors add up to 297600; without 82320 itself that is 215280, so 82320 is abundant (215280 is more than 82320). Euler's totient φ(82320) = 18816 numbers up to 82320 share no factor with it.
4
The digits of 82320 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 63 steps to reach 1.

LaTeX source of the formulas on this page

\[ 82320 = 2^{4} \times 3 \times 5 \times 7^{3} \]

82320 at a glance

Property	Value
Type	composite
Number of divisors	80
Sum of divisors	297600
Euler totient φ(n)	18816
Square	6776582400
Cube	557848263168000
Square root	286.914621 (= 28√105)
Digit sum / digital root	15 / 6
Collatz steps to 1	63
Scientific notation	8.232 × $10^{4}$

82320 in other forms

Form	Value
In words	eighty-two thousand three hundred and twenty
Binary (base 2)	10100000110010000
Octal (base 8)	240620
Hexadecimal (base 16)	14190
Base 3	11011220220
As time	82320 seconds = 22 h 52 min 0 s

Is 82320 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (82320 ÷ 2 = 41160)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (82320 ÷ 3 = 27440)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (82320 ÷ 4 = 20580)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (82320 ÷ 5 = 16464)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (82320 ÷ 6 = 13720)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (82320 ÷ 7 = 11760)	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 (82320 ÷ 8 = 10290)	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 (82320 ÷ 10 = 8232)	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 (82320 ÷ 12 = 6860)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 82320 a prime number?

No. 82320 = $2^{4}$ × 3 × 5 × $7^{3}$ , so it is divisible by 2.

What are the factors of 82320?

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 49, 56, 60, 70, 80, 84, 98, 105, 112, 120, 140, 147, 168, 196, 210, 240, 245, 280, 294, 336, 343, 392, 420, 490, 560, 588, 686, 735, 784, 840, 980, 1029, 1176, 1372, 1470, 1680, 1715, 1960, 2058, 2352, 2744, 2940, 3430, 3920, 4116, 5145, 5488, 5880, 6860, 8232, 10290, 11760, 13720, 16464, 20580, 27440, 41160, 82320.

What is 82320 in binary?

10100000110010000 (hexadecimal 14190, octal 240620).

What is the square root of 82320?

About 286.9146, exactly 28√105.

Is 82320 divisible by 3?

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

What is special about the number 82320?

82320 is a Harshad number: divisible by its digit sum 15.