The number 90804

Q: Is 90804 a prime number?

No. 90804 = 2^2 × 3 × 7 × 23 × 47, so it is divisible by 2.

90804 is a composite number with 48 divisors. Its prime factorisation is $2^{2}$ × 3 × 7 × 23 × 47. Divisors (48): 1, 2, 3, 4, 6, 7, 12, 14, 21, 23, 28, 42, 46, 47, 69, 84 … 90804.

Number

Pick any whole number from 1 to 100,000.

90804 = 2^{2} \times 3 \times 7 \times 23 \times 47

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How to work it out

1
What is special about 90804: a Harshad number: divisible by its digit sum 21.
2
90804 is composite. Its prime factorisation is
$90804 = 2^{2} \times 3 \times 7 \times 23 \times 47$
3
The divisors add up to 258048; without 90804 itself that is 167244, so 90804 is abundant (167244 is more than 90804). Euler's totient φ(90804) = 24288 numbers up to 90804 share no factor with it.
4
The digits of 90804 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 133 steps to reach 1.

LaTeX source of the formulas on this page

\[ 90804 = 2^{2} \times 3 \times 7 \times 23 \times 47 \]

90804 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	258048
Euler totient φ(n)	24288
Square	8245366416
Cube	748712252038464
Square root	301.337021 (= 2√22701)
Digit sum / digital root	21 / 3
Collatz steps to 1	133
Scientific notation	9.0804 × $10^{4}$

90804 in other forms

Form	Value
In words	ninety thousand eight hundred and four
Binary (base 2)	10110001010110100
Octal (base 8)	261264
Hexadecimal (base 16)	162B4
Base 3	11121120010
As time	90804 seconds = 25 h 13 min 24 s

Is 90804 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (90804 ÷ 2 = 45402)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (90804 ÷ 3 = 30268)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (90804 ÷ 4 = 22701)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 4)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (90804 ÷ 6 = 15134)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (90804 ÷ 7 = 12972)	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	No (remainder 3)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 4)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 10)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (90804 ÷ 12 = 7567)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 90804 a prime number?

No. 90804 = $2^{2}$ × 3 × 7 × 23 × 47, so it is divisible by 2.

What are the factors of 90804?

1, 2, 3, 4, 6, 7, 12, 14, 21, 23, 28, 42, 46, 47, 69, 84, 92, 94, 138, 141, 161, 188, 276, 282, 322, 329, 483, 564, 644, 658, 966, 987, 1081, 1316, 1932, 1974, 2162, 3243, 3948, 4324, 6486, 7567, 12972, 15134, 22701, 30268, 45402, 90804.

What is 90804 in binary?

10110001010110100 (hexadecimal 162B4, octal 261264).

What is the square root of 90804?

About 301.3370, exactly 2√22701.

Is 90804 divisible by 3?

Yes. Its digits add up to 21, a multiple of 3.

What is special about the number 90804?

90804 is a Harshad number: divisible by its digit sum 21.