The number 82200

Q: Is 82200 a prime number?

No. 82200 = 2^3 × 3 × 5^2 × 137, so it is divisible by 2.

82200 is a composite number with 48 divisors. Its prime factorisation is $2^{3}$ × 3 × $5^{2}$ × 137. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50 … 82200.

Number

Pick any whole number from 1 to 100,000.

82200 = 2^{3} \times 3 \times 5^{2} \times 137

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How to work it out

1
What is special about 82200: a Harshad number: divisible by its digit sum 12.
2
82200 is composite. Its prime factorisation is
$82200 = 2^{3} \times 3 \times 5^{2} \times 137$
3
The divisors add up to 256680; without 82200 itself that is 174480, so 82200 is abundant (174480 is more than 82200). Euler's totient φ(82200) = 21760 numbers up to 82200 share no factor with it.
4
The digits of 82200 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 58 steps to reach 1.

LaTeX source of the formulas on this page

\[ 82200 = 2^{3} \times 3 \times 5^{2} \times 137 \]

82200 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	256680
Euler totient φ(n)	21760
Square	6756840000
Cube	555412248000000
Square root	286.705424 (= 10√822)
Digit sum / digital root	12 / 3
Collatz steps to 1	58
Scientific notation	8.22 × $10^{4}$

82200 in other forms

Form	Value
In words	eighty-two thousand two hundred
Binary (base 2)	10100000100011000
Octal (base 8)	240430
Hexadecimal (base 16)	14118
Base 3	11011202110
As time	82200 seconds = 22 h 50 min 0 s

Is 82200 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (82200 ÷ 2 = 41100)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (82200 ÷ 3 = 27400)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (82200 ÷ 4 = 20550)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (82200 ÷ 5 = 16440)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (82200 ÷ 6 = 13700)	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 (82200 ÷ 8 = 10275)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 3)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (82200 ÷ 10 = 8220)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 8)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (82200 ÷ 12 = 6850)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 82200 a prime number?

No. 82200 = $2^{3}$ × 3 × $5^{2}$ × 137, so it is divisible by 2.

What are the factors of 82200?

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 137, 150, 200, 274, 300, 411, 548, 600, 685, 822, 1096, 1370, 1644, 2055, 2740, 3288, 3425, 4110, 5480, 6850, 8220, 10275, 13700, 16440, 20550, 27400, 41100, 82200.

What is 82200 in binary?

10100000100011000 (hexadecimal 14118, octal 240430).

What is the square root of 82200?

About 286.7054, exactly 10√822.

Is 82200 divisible by 3?

Yes. Its digits add up to 12, a multiple of 3.

What is special about the number 82200?

82200 is a Harshad number: divisible by its digit sum 12.