The number 90900

Q: Is 90900 a prime number?

No. 90900 = 2^2 × 3^2 × 5^2 × 101, so it is divisible by 2.

90900 is a composite number with 54 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × $5^{2}$ × 101. Divisors (54): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45 … 90900.

Number

Pick any whole number from 1 to 100,000.

90900 = 2^{2} \times 3^{2} \times 5^{2} \times 101

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How to work it out

1
What is special about 90900: a Harshad number: divisible by its digit sum 18.
2
90900 is composite. Its prime factorisation is
$90900 = 2^{2} \times 3^{2} \times 5^{2} \times 101$
3
The divisors add up to 287742; without 90900 itself that is 196842, so 90900 is abundant (196842 is more than 90900). Euler's totient φ(90900) = 24000 numbers up to 90900 share no factor with it.
4
The digits of 90900 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 84 steps to reach 1.

LaTeX source of the formulas on this page

\[ 90900 = 2^{2} \times 3^{2} \times 5^{2} \times 101 \]

90900 at a glance

Property	Value
Type	composite
Number of divisors	54
Sum of divisors	287742
Euler totient φ(n)	24000
Square	8262810000
Cube	751089429000000
Square root	301.496269 (= 30√101)
Digit sum / digital root	18 / 9
Collatz steps to 1	84
Scientific notation	9.09 × $10^{4}$

90900 in other forms

Form	Value
In words	ninety thousand nine hundred
Binary (base 2)	10110001100010100
Octal (base 8)	261424
Hexadecimal (base 16)	16314
Base 3	11121200200
As time	90900 seconds = 25 h 15 min 0 s

Is 90900 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (90900 ÷ 2 = 45450)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (90900 ÷ 3 = 30300)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (90900 ÷ 4 = 22725)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (90900 ÷ 5 = 18180)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (90900 ÷ 6 = 15150)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 5)	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 (90900 ÷ 9 = 10100)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (90900 ÷ 10 = 9090)	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 (90900 ÷ 12 = 7575)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 90900 a prime number?

No. 90900 = $2^{2}$ × $3^{2}$ × $5^{2}$ × 101, so it is divisible by 2.

What are the factors of 90900?

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 101, 150, 180, 202, 225, 300, 303, 404, 450, 505, 606, 900, 909, 1010, 1212, 1515, 1818, 2020, 2525, 3030, 3636, 4545, 5050, 6060, 7575, 9090, 10100, 15150, 18180, 22725, 30300, 45450, 90900.

What is 90900 in binary?

10110001100010100 (hexadecimal 16314, octal 261424).

What is the square root of 90900?

About 301.4963, exactly 30√101.

Is 90900 divisible by 3?

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

What is special about the number 90900?

90900 is a Harshad number: divisible by its digit sum 18.