The number 16380

Q: Is 16380 a prime number?

No. 16380 = 2^2 × 3^2 × 5 × 7 × 13, so it is divisible by 2.

16380 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × 5 × 7 × 13. Divisors (72): 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 14, 15, 18, 20, 21 … 16380.

Number

Pick any whole number from 1 to 100,000.

16380 = 2^{2} \times 3^{2} \times 5 \times 7 \times 13

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How to work it out

1
What is special about 16380: a Harshad number: divisible by its digit sum 18.
2
16380 is composite. Its prime factorisation is
$16380 = 2^{2} \times 3^{2} \times 5 \times 7 \times 13$
3
The divisors add up to 61152; without 16380 itself that is 44772, so 16380 is abundant (44772 is more than 16380). Euler's totient φ(16380) = 3456 numbers up to 16380 share no factor with it.
4
The digits of 16380 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 159 steps to reach 1.

LaTeX source of the formulas on this page

\[ 16380 = 2^{2} \times 3^{2} \times 5 \times 7 \times 13 \]

16380 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	61152
Euler totient φ(n)	3456
Square	268304400
Cube	4394826072000
Square root	127.984374 (= 6√455)
Digit sum / digital root	18 / 9
Collatz steps to 1	159
Scientific notation	1.638 × $10^{4}$

16380 in other forms

Form	Value
In words	sixteen thousand three hundred and eighty
Binary (base 2)	11111111111100
Octal (base 8)	37774
Hexadecimal (base 16)	3FFC
Base 3	211110200
As time	16380 seconds = 4 h 33 min 0 s

Is 16380 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (16380 ÷ 2 = 8190)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (16380 ÷ 3 = 5460)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (16380 ÷ 4 = 4095)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (16380 ÷ 5 = 3276)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (16380 ÷ 6 = 2730)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (16380 ÷ 7 = 2340)	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 (16380 ÷ 9 = 1820)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (16380 ÷ 10 = 1638)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 1)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (16380 ÷ 12 = 1365)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 16380 a prime number?

No. 16380 = $2^{2}$ × $3^{2}$ × 5 × 7 × 13, so it is divisible by 2.

What are the factors of 16380?

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 14, 15, 18, 20, 21, 26, 28, 30, 35, 36, 39, 42, 45, 52, 60, 63, 65, 70, 78, 84, 90, 91, 105, 117, 126, 130, 140, 156, 180, 182, 195, 210, 234, 252, 260, 273, 315, 364, 390, 420, 455, 468, 546, 585, 630, 780, 819, 910, 1092, 1170, 1260, 1365, 1638, 1820, 2340, 2730, 3276, 4095, 5460, 8190, 16380.

What is 16380 in binary?

11111111111100 (hexadecimal 3FFC, octal 37774).

What is the square root of 16380?

About 127.9844, exactly 6√455.

Is 16380 divisible by 3?

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

What is special about the number 16380?

16380 is a Harshad number: divisible by its digit sum 18.