The number 13860

Q: Is 13860 a prime number?

No. 13860 = 2^2 × 3^2 × 5 × 7 × 11, so it is divisible by 2.

13860 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × 5 × 7 × 11. Divisors (72): 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 18, 20, 21 … 13860.

Number

Pick any whole number from 1 to 100,000.

13860 = 2^{2} \times 3^{2} \times 5 \times 7 \times 11

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How to work it out

1
What is special about 13860: a Harshad number: divisible by its digit sum 18.
2
13860 is composite. Its prime factorisation is
$13860 = 2^{2} \times 3^{2} \times 5 \times 7 \times 11$
3
The divisors add up to 52416; without 13860 itself that is 38556, so 13860 is abundant (38556 is more than 13860). Euler's totient φ(13860) = 2880 numbers up to 13860 share no factor with it.
4
The digits of 13860 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 151 steps to reach 1.

LaTeX source of the formulas on this page

\[ 13860 = 2^{2} \times 3^{2} \times 5 \times 7 \times 11 \]

13860 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	52416
Euler totient φ(n)	2880
Square	192099600
Cube	2662500456000
Square root	117.728501 (= 6√385)
Digit sum / digital root	18 / 9
Collatz steps to 1	151
Scientific notation	1.386 × $10^{4}$

13860 in other forms

Form	Value
In words	thirteen thousand eight hundred and sixty
Binary (base 2)	11011000100100
Octal (base 8)	33044
Hexadecimal (base 16)	3624
Base 3	201000100
As time	13860 seconds = 3 h 51 min 0 s

Is 13860 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (13860 ÷ 2 = 6930)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (13860 ÷ 3 = 4620)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (13860 ÷ 4 = 3465)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (13860 ÷ 5 = 2772)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (13860 ÷ 6 = 2310)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (13860 ÷ 7 = 1980)	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 (13860 ÷ 9 = 1540)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (13860 ÷ 10 = 1386)	A number is divisible by 10 if the last digit is 0.
11	Yes (13860 ÷ 11 = 1260)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (13860 ÷ 12 = 1155)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 13860 a prime number?

No. 13860 = $2^{2}$ × $3^{2}$ × 5 × 7 × 11, so it is divisible by 2.

What are the factors of 13860?

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 18, 20, 21, 22, 28, 30, 33, 35, 36, 42, 44, 45, 55, 60, 63, 66, 70, 77, 84, 90, 99, 105, 110, 126, 132, 140, 154, 165, 180, 198, 210, 220, 231, 252, 308, 315, 330, 385, 396, 420, 462, 495, 630, 660, 693, 770, 924, 990, 1155, 1260, 1386, 1540, 1980, 2310, 2772, 3465, 4620, 6930, 13860.

What is 13860 in binary?

11011000100100 (hexadecimal 3624, octal 33044).

What is the square root of 13860?

About 117.7285, exactly 6√385.

Is 13860 divisible by 3?

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

What is special about the number 13860?

13860 is a Harshad number: divisible by its digit sum 18.