The number 88200

Q: Is 88200 a prime number?

No. 88200 = 2^3 × 3^2 × 5^2 × 7^2, so it is divisible by 2.

88200 is a composite number with 108 divisors. Its prime factorisation is $2^{3}$ × $3^{2}$ × $5^{2}$ × $7^{2}$ . Divisors (108): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21 … 88200.

Number

Pick any whole number from 1 to 100,000.

88200 = 2^{3} \times 3^{2} \times 5^{2} \times 7^{2}

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How to work it out

1
What is special about 88200: a Harshad number: divisible by its digit sum 18.
2
88200 is composite. Its prime factorisation is
$88200 = 2^{3} \times 3^{2} \times 5^{2} \times 7^{2}$
3
The divisors add up to 344565; without 88200 itself that is 256365, so 88200 is abundant (256365 is more than 88200). Euler's totient φ(88200) = 20160 numbers up to 88200 share no factor with it.
4
The digits of 88200 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 164 steps to reach 1.

LaTeX source of the formulas on this page

\[ 88200 = 2^{3} \times 3^{2} \times 5^{2} \times 7^{2} \]

88200 at a glance

Property	Value
Type	composite
Number of divisors	108
Sum of divisors	344565
Euler totient φ(n)	20160
Square	7779240000
Cube	686128968000000
Square root	296.984848 (= 210√2)
Digit sum / digital root	18 / 9
Collatz steps to 1	164
Scientific notation	8.82 × $10^{4}$

88200 in other forms

Form	Value
In words	eighty-eight thousand two hundred
Binary (base 2)	10101100010001000
Octal (base 8)	254210
Hexadecimal (base 16)	15888
Base 3	11110222200
As time	88200 seconds = 24 h 30 min 0 s

Is 88200 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (88200 ÷ 2 = 44100)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (88200 ÷ 3 = 29400)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (88200 ÷ 4 = 22050)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (88200 ÷ 5 = 17640)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (88200 ÷ 6 = 14700)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (88200 ÷ 7 = 12600)	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 (88200 ÷ 8 = 11025)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (88200 ÷ 9 = 9800)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (88200 ÷ 10 = 8820)	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 (88200 ÷ 12 = 7350)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 88200 a prime number?

No. 88200 = $2^{3}$ × $3^{2}$ × $5^{2}$ × $7^{2}$ , so it is divisible by 2.

What are the factors of 88200?

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 25, 28, 30, 35, 36, 40, 42, 45, 49, 50, 56, 60, 63, 70, 72, 75, 84, 90, 98, 100, 105, 120, 126, 140, 147, 150, 168, 175, 180, 196, 200, 210, 225, 245, 252, 280, 294, 300, 315, 350, 360, 392, 420, 441, 450, 490, 504, 525, 588, 600, 630, 700, 735, 840, 882, 900, 980, 1050, 1176, 1225, 1260, 1400, 1470, 1575, 1764, 1800, 1960, 2100, 2205, 2450, 2520, 2940, 3150, 3528, 3675, 4200, 4410, 4900, 5880, 6300, 7350, 8820, 9800, 11025, 12600, 14700, 17640, 22050, 29400, 44100, 88200.

What is 88200 in binary?

10101100010001000 (hexadecimal 15888, octal 254210).

What is the square root of 88200?

About 296.9848, exactly 210√2.

Is 88200 divisible by 3?

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

What is special about the number 88200?

88200 is a Harshad number: divisible by its digit sum 18.