The number 90828

Q: Is 90828 a prime number?

No. 90828 = 2^2 × 3^3 × 29^2, so it is divisible by 2.

90828 is a composite number with 36 divisors. Its prime factorisation is $2^{2}$ × $3^{3}$ × $29^{2}$ . Divisors (36): 1, 2, 3, 4, 6, 9, 12, 18, 27, 29, 36, 54, 58, 87, 108, 116 … 90828.

Number

Pick any whole number from 1 to 100,000.

90828 = 2^{2} \times 3^{3} \times 29^{2}

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How to work it out

1
What is special about 90828: a Harshad number: divisible by its digit sum 27.
2
90828 is composite. Its prime factorisation is
$90828 = 2^{2} \times 3^{3} \times 29^{2}$
3
The divisors add up to 243880; without 90828 itself that is 153052, so 90828 is abundant (153052 is more than 90828). Euler's totient φ(90828) = 29232 numbers up to 90828 share no factor with it.
4
The digits of 90828 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 45 steps to reach 1.

LaTeX source of the formulas on this page

\[ 90828 = 2^{2} \times 3^{3} \times 29^{2} \]

90828 at a glance

Property	Value
Type	composite
Number of divisors	36
Sum of divisors	243880
Euler totient φ(n)	29232
Square	8249725584
Cube	749306075343552
Square root	301.376841 (= 174√3)
Digit sum / digital root	27 / 9
Collatz steps to 1	45
Scientific notation	9.0828 × $10^{4}$

90828 in other forms

Form	Value
In words	ninety thousand eight hundred and twenty-eight
Binary (base 2)	10110001011001100
Octal (base 8)	261314
Hexadecimal (base 16)	162CC
Base 3	11121121000
As time	90828 seconds = 25 h 13 min 48 s

Is 90828 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (90828 ÷ 2 = 45414)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (90828 ÷ 3 = 30276)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (90828 ÷ 4 = 22707)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 3)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (90828 ÷ 6 = 15138)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 3)	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	No (remainder 4)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (90828 ÷ 9 = 10092)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 8)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 1)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (90828 ÷ 12 = 7569)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 90828 a prime number?

No. 90828 = $2^{2}$ × $3^{3}$ × $29^{2}$ , so it is divisible by 2.

What are the factors of 90828?

1, 2, 3, 4, 6, 9, 12, 18, 27, 29, 36, 54, 58, 87, 108, 116, 174, 261, 348, 522, 783, 841, 1044, 1566, 1682, 2523, 3132, 3364, 5046, 7569, 10092, 15138, 22707, 30276, 45414, 90828.

What is 90828 in binary?

10110001011001100 (hexadecimal 162CC, octal 261314).

What is the square root of 90828?

About 301.3768, exactly 174√3.

Is 90828 divisible by 3?

Yes. Its digits add up to 27, a multiple of 3.

What is special about the number 90828?

90828 is a Harshad number: divisible by its digit sum 27.