The number 53820

Q: Is 53820 a prime number?

No. 53820 = 2^2 × 3^2 × 5 × 13 × 23, so it is divisible by 2.

53820 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × 5 × 13 × 23. Divisors (72): 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 23, 26, 30 … 53820.

Number

Pick any whole number from 1 to 100,000.

53820 = 2^{2} \times 3^{2} \times 5 \times 13 \times 23

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How to work it out

1
What is special about 53820: a Harshad number: divisible by its digit sum 18.
2
53820 is composite. Its prime factorisation is
$53820 = 2^{2} \times 3^{2} \times 5 \times 13 \times 23$
3
The divisors add up to 183456; without 53820 itself that is 129636, so 53820 is abundant (129636 is more than 53820). Euler's totient φ(53820) = 12672 numbers up to 53820 share no factor with it.
4
The digits of 53820 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 52 steps to reach 1.

LaTeX source of the formulas on this page

\[ 53820 = 2^{2} \times 3^{2} \times 5 \times 13 \times 23 \]

53820 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	183456
Euler totient φ(n)	12672
Square	2896592400
Cube	155894602968000
Square root	231.991379 (= 6√1495)
Digit sum / digital root	18 / 9
Collatz steps to 1	52
Scientific notation	5.382 × $10^{4}$

53820 in other forms

Form	Value
In words	fifty-three thousand eight hundred and twenty
Binary (base 2)	1101001000111100
Octal (base 8)	151074
Hexadecimal (base 16)	D23C
Base 3	2201211100
As time	53820 seconds = 14 h 57 min 0 s

Is 53820 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (53820 ÷ 2 = 26910)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (53820 ÷ 3 = 17940)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (53820 ÷ 4 = 13455)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (53820 ÷ 5 = 10764)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (53820 ÷ 6 = 8970)	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	No (remainder 4)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (53820 ÷ 9 = 5980)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (53820 ÷ 10 = 5382)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 8)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (53820 ÷ 12 = 4485)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 53820 a prime number?

No. 53820 = $2^{2}$ × $3^{2}$ × 5 × 13 × 23, so it is divisible by 2.

What are the factors of 53820?

1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 23, 26, 30, 36, 39, 45, 46, 52, 60, 65, 69, 78, 90, 92, 115, 117, 130, 138, 156, 180, 195, 207, 230, 234, 260, 276, 299, 345, 390, 414, 460, 468, 585, 598, 690, 780, 828, 897, 1035, 1170, 1196, 1380, 1495, 1794, 2070, 2340, 2691, 2990, 3588, 4140, 4485, 5382, 5980, 8970, 10764, 13455, 17940, 26910, 53820.

What is 53820 in binary?

1101001000111100 (hexadecimal D23C, octal 151074).

What is the square root of 53820?

About 231.9914, exactly 6√1495.

Is 53820 divisible by 3?

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

What is special about the number 53820?

53820 is a Harshad number: divisible by its digit sum 18.