The number 90000

Q: Is 90000 a prime number?

No. 90000 = 2^4 × 3^2 × 5^4, so it is divisible by 2.

90000 is a perfect square (300²). Its prime factorisation is $2^{4}$ × $3^{2}$ × $5^{4}$ . Divisors (75): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25 … 90000.

Number

Pick any whole number from 1 to 100,000.

90000 = 2^{4} \times 3^{2} \times 5^{4}

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How to work it out

1
What is special about 90000: a perfect square (300²); a Harshad number: divisible by its digit sum 9.
2
90000 is composite. Its prime factorisation is
$90000 = 2^{4} \times 3^{2} \times 5^{4}$
3
The divisors add up to 314743; without 90000 itself that is 224743, so 90000 is abundant (224743 is more than 90000). Euler's totient φ(90000) = 24000 numbers up to 90000 share no factor with it.
4
The digits of 90000 add up to 9, 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

\[ 90000 = 2^{4} \times 3^{2} \times 5^{4} \]

90000 at a glance

Property	Value
Type	composite
Number of divisors	75
Sum of divisors	314743
Euler totient φ(n)	24000
Square	8100000000
Cube	729000000000000
Square root	300
Digit sum / digital root	9 / 9
Collatz steps to 1	164
Scientific notation	9 × $10^{4}$
Perfect power	$300^{2}$

90000 in other forms

Form	Value
In words	ninety thousand
Binary (base 2)	10101111110010000
Octal (base 8)	257620
Hexadecimal (base 16)	15F90
Base 3	11120110100
As time	90000 seconds = 25 h 0 min 0 s

Is 90000 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (90000 ÷ 2 = 45000)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (90000 ÷ 3 = 30000)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (90000 ÷ 4 = 22500)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (90000 ÷ 5 = 18000)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (90000 ÷ 6 = 15000)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 1)	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 (90000 ÷ 8 = 11250)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (90000 ÷ 9 = 10000)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (90000 ÷ 10 = 9000)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 9)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (90000 ÷ 12 = 7500)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 90000 a prime number?

No. 90000 = $2^{4}$ × $3^{2}$ × $5^{4}$ , so it is divisible by 2.

What are the factors of 90000?

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 125, 144, 150, 180, 200, 225, 240, 250, 300, 360, 375, 400, 450, 500, 600, 625, 720, 750, 900, 1000, 1125, 1200, 1250, 1500, 1800, 1875, 2000, 2250, 2500, 3000, 3600, 3750, 4500, 5000, 5625, 6000, 7500, 9000, 10000, 11250, 15000, 18000, 22500, 30000, 45000, 90000.

What is 90000 in binary?

10101111110010000 (hexadecimal 15F90, octal 257620).

What is the square root of 90000?

300, because 300 × 300 = 90000.

Is 90000 divisible by 3?

Yes. Its digits add up to 9, a multiple of 3.

What is special about the number 90000?

90000 is a perfect square (300²); a Harshad number: divisible by its digit sum 9.