The number 38280

Q: Is 38280 a prime number?

No. 38280 = 2^3 × 3 × 5 × 11 × 29, so it is divisible by 2.

38280 is a composite number with 64 divisors. Its prime factorisation is $2^{3}$ × 3 × 5 × 11 × 29. Divisors (64): 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 29, 30 … 38280.

Number

Pick any whole number from 1 to 100,000.

38280 = 2^{3} \times 3 \times 5 \times 11 \times 29

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How to work it out

1
38280 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
38280 is composite. Its prime factorisation is
$38280 = 2^{3} \times 3 \times 5 \times 11 \times 29$
3
The divisors add up to 129600; without 38280 itself that is 91320, so 38280 is abundant (91320 is more than 38280). Euler's totient φ(38280) = 8960 numbers up to 38280 share no factor with it.
4
The digits of 38280 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 75 steps to reach 1.

LaTeX source of the formulas on this page

\[ 38280 = 2^{3} \times 3 \times 5 \times 11 \times 29 \]

38280 at a glance

Property	Value
Type	composite
Number of divisors	64
Sum of divisors	129600
Euler totient φ(n)	8960
Square	1465358400
Cube	56093919552000
Square root	195.652754 (= 2√9570)
Digit sum / digital root	21 / 3
Collatz steps to 1	75
Scientific notation	3.828 × $10^{4}$

38280 in other forms

Form	Value
In words	thirty-eight thousand two hundred and eighty
Binary (base 2)	1001010110001000
Octal (base 8)	112610
Hexadecimal (base 16)	9588
Base 3	1221111210
As time	38280 seconds = 10 h 38 min 0 s

Is 38280 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (38280 ÷ 2 = 19140)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (38280 ÷ 3 = 12760)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (38280 ÷ 4 = 9570)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (38280 ÷ 5 = 7656)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (38280 ÷ 6 = 6380)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 4)	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 (38280 ÷ 8 = 4785)	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	Yes (38280 ÷ 10 = 3828)	A number is divisible by 10 if the last digit is 0.
11	Yes (38280 ÷ 11 = 3480)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (38280 ÷ 12 = 3190)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 38280 a prime number?

No. 38280 = $2^{3}$ × 3 × 5 × 11 × 29, so it is divisible by 2.

What are the factors of 38280?

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 29, 30, 33, 40, 44, 55, 58, 60, 66, 87, 88, 110, 116, 120, 132, 145, 165, 174, 220, 232, 264, 290, 319, 330, 348, 435, 440, 580, 638, 660, 696, 870, 957, 1160, 1276, 1320, 1595, 1740, 1914, 2552, 3190, 3480, 3828, 4785, 6380, 7656, 9570, 12760, 19140, 38280.

What is 38280 in binary?

1001010110001000 (hexadecimal 9588, octal 112610).

What is the square root of 38280?

About 195.6528, exactly 2√9570.

Is 38280 divisible by 3?

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

What is special about the number 38280?

It is a composite number with 64 divisors.