The number 21780

Q: Is 21780 a prime number?

No. 21780 = 2^2 × 3^2 × 5 × 11^2, so it is divisible by 2.

21780 is a composite number with 54 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × 5 × $11^{2}$ . Divisors (54): 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33 … 21780.

Number

Pick any whole number from 1 to 100,000.

21780 = 2^{2} \times 3^{2} \times 5 \times 11^{2}

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How to work it out

1
What is special about 21780: a Harshad number: divisible by its digit sum 18.
2
21780 is composite. Its prime factorisation is
$21780 = 2^{2} \times 3^{2} \times 5 \times 11^{2}$
3
The divisors add up to 72618; without 21780 itself that is 50838, so 21780 is abundant (50838 is more than 21780). Euler's totient φ(21780) = 5280 numbers up to 21780 share no factor with it.
4
The digits of 21780 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 56 steps to reach 1.

LaTeX source of the formulas on this page

\[ 21780 = 2^{2} \times 3^{2} \times 5 \times 11^{2} \]

21780 at a glance

Property	Value
Type	composite
Number of divisors	54
Sum of divisors	72618
Euler totient φ(n)	5280
Square	474368400
Cube	10331743752000
Square root	147.580487 (= 66√5)
Digit sum / digital root	18 / 9
Collatz steps to 1	56
Scientific notation	2.178 × $10^{4}$

21780 in other forms

Form	Value
In words	twenty-one thousand seven hundred and eighty
Binary (base 2)	101010100010100
Octal (base 8)	52424
Hexadecimal (base 16)	5514
Base 3	1002212200
As time	21780 seconds = 6 h 3 min 0 s

Is 21780 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (21780 ÷ 2 = 10890)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (21780 ÷ 3 = 7260)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (21780 ÷ 4 = 5445)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (21780 ÷ 5 = 4356)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (21780 ÷ 6 = 3630)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 3)	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 (21780 ÷ 9 = 2420)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (21780 ÷ 10 = 2178)	A number is divisible by 10 if the last digit is 0.
11	Yes (21780 ÷ 11 = 1980)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (21780 ÷ 12 = 1815)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 21780 a prime number?

No. 21780 = $2^{2}$ × $3^{2}$ × 5 × $11^{2}$ , so it is divisible by 2.

What are the factors of 21780?

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 121, 132, 165, 180, 198, 220, 242, 330, 363, 396, 484, 495, 605, 660, 726, 990, 1089, 1210, 1452, 1815, 1980, 2178, 2420, 3630, 4356, 5445, 7260, 10890, 21780.

What is 21780 in binary?

101010100010100 (hexadecimal 5514, octal 52424).

What is the square root of 21780?

About 147.5805, exactly 66√5.

Is 21780 divisible by 3?

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

What is special about the number 21780?

21780 is a Harshad number: divisible by its digit sum 18.