The number 40500

Q: Is 40500 a prime number?

No. 40500 = 2^2 × 3^4 × 5^3, so it is divisible by 2.

40500 is a composite number with 60 divisors. Its prime factorisation is $2^{2}$ × $3^{4}$ × $5^{3}$ . Divisors (60): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36 … 40500.

Number

Pick any whole number from 1 to 100,000.

40500 = 2^{2} \times 3^{4} \times 5^{3}

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How to work it out

1
What is special about 40500: a Harshad number: divisible by its digit sum 9.
2
40500 is composite. Its prime factorisation is
$40500 = 2^{2} \times 3^{4} \times 5^{3}$
3
The divisors add up to 132132; without 40500 itself that is 91632, so 40500 is abundant (91632 is more than 40500). Euler's totient φ(40500) = 10800 numbers up to 40500 share no factor with it.
4
The digits of 40500 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 44 steps to reach 1.

LaTeX source of the formulas on this page

\[ 40500 = 2^{2} \times 3^{4} \times 5^{3} \]

40500 at a glance

Property	Value
Type	composite
Number of divisors	60
Sum of divisors	132132
Euler totient φ(n)	10800
Square	1640250000
Cube	66430125000000
Square root	201.246118 (= 90√5)
Digit sum / digital root	9 / 9
Collatz steps to 1	44
Scientific notation	4.05 × $10^{4}$

40500 in other forms

Form	Value
In words	forty thousand five hundred
Binary (base 2)	1001111000110100
Octal (base 8)	117064
Hexadecimal (base 16)	9E34
Base 3	2001120000
As time	40500 seconds = 11 h 15 min 0 s

Is 40500 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (40500 ÷ 2 = 20250)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (40500 ÷ 3 = 13500)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (40500 ÷ 4 = 10125)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (40500 ÷ 5 = 8100)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (40500 ÷ 6 = 6750)	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 (40500 ÷ 9 = 4500)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (40500 ÷ 10 = 4050)	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 (40500 ÷ 12 = 3375)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 40500 a prime number?

No. 40500 = $2^{2}$ × $3^{4}$ × $5^{3}$ , so it is divisible by 2.

What are the factors of 40500?

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 81, 90, 100, 108, 125, 135, 150, 162, 180, 225, 250, 270, 300, 324, 375, 405, 450, 500, 540, 675, 750, 810, 900, 1125, 1350, 1500, 1620, 2025, 2250, 2700, 3375, 4050, 4500, 6750, 8100, 10125, 13500, 20250, 40500.

What is 40500 in binary?

1001111000110100 (hexadecimal 9E34, octal 117064).

What is the square root of 40500?

About 201.2461, exactly 90√5.

Is 40500 divisible by 3?

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

What is special about the number 40500?

40500 is a Harshad number: divisible by its digit sum 9.