The number 41580

Q: Is 41580 a prime number?

No. 41580 = 2^2 × 3^3 × 5 × 7 × 11, so it is divisible by 2.

41580 is a composite number with 96 divisors. Its prime factorisation is $2^{2}$ × $3^{3}$ × 5 × 7 × 11. Divisors (96): 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 18, 20, 21 … 41580.

Number

Pick any whole number from 1 to 100,000.

41580 = 2^{2} \times 3^{3} \times 5 \times 7 \times 11

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How to work it out

1
What is special about 41580: a Harshad number: divisible by its digit sum 18.
2
41580 is composite. Its prime factorisation is
$41580 = 2^{2} \times 3^{3} \times 5 \times 7 \times 11$
3
The divisors add up to 161280; without 41580 itself that is 119700, so 41580 is abundant (119700 is more than 41580). Euler's totient φ(41580) = 8640 numbers up to 41580 share no factor with it.
4
The digits of 41580 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 88 steps to reach 1.

LaTeX source of the formulas on this page

\[ 41580 = 2^{2} \times 3^{3} \times 5 \times 7 \times 11 \]

41580 at a glance

Property	Value
Type	composite
Number of divisors	96
Sum of divisors	161280
Euler totient φ(n)	8640
Square	1728896400
Cube	71887512312000
Square root	203.911746 (= 6√1155)
Digit sum / digital root	18 / 9
Collatz steps to 1	88
Scientific notation	4.158 × $10^{4}$

41580 in other forms

Form	Value
In words	forty-one thousand five hundred and eighty
Binary (base 2)	1010001001101100
Octal (base 8)	121154
Hexadecimal (base 16)	A26C
Base 3	2010001000
As time	41580 seconds = 11 h 33 min 0 s

Is 41580 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (41580 ÷ 2 = 20790)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (41580 ÷ 3 = 13860)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (41580 ÷ 4 = 10395)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (41580 ÷ 5 = 8316)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (41580 ÷ 6 = 6930)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (41580 ÷ 7 = 5940)	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 (41580 ÷ 9 = 4620)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (41580 ÷ 10 = 4158)	A number is divisible by 10 if the last digit is 0.
11	Yes (41580 ÷ 11 = 3780)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (41580 ÷ 12 = 3465)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 41580 a prime number?

No. 41580 = $2^{2}$ × $3^{3}$ × 5 × 7 × 11, so it is divisible by 2.

What are the factors of 41580?

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 18, 20, 21, 22, 27, 28, 30, 33, 35, 36, 42, 44, 45, 54, 55, 60, 63, 66, 70, 77, 84, 90, 99, 105, 108, 110, 126, 132, 135, 140, 154, 165, 180, 189, 198, 210, 220, 231, 252, 270, 297, 308, 315, 330, 378, 385, 396, 420, 462, 495, 540, 594, 630, 660, 693, 756, 770, 924, 945, 990, 1155, 1188, 1260, 1386, 1485, 1540, 1890, 1980, 2079, 2310, 2772, 2970, 3465, 3780, 4158, 4620, 5940, 6930, 8316, 10395, 13860, 20790, 41580.

What is 41580 in binary?

1010001001101100 (hexadecimal A26C, octal 121154).

What is the square root of 41580?

About 203.9117, exactly 6√1155.

Is 41580 divisible by 3?

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

What is special about the number 41580?

41580 is a Harshad number: divisible by its digit sum 18.