The number 53040

Q: Is 53040 a prime number?

No. 53040 = 2^4 × 3 × 5 × 13 × 17, so it is divisible by 2.

53040 is a composite number with 80 divisors. Its prime factorisation is $2^{4}$ × 3 × 5 × 13 × 17. Divisors (80): 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 17, 20, 24, 26 … 53040.

Number

Pick any whole number from 1 to 100,000.

53040 = 2^{4} \times 3 \times 5 \times 13 \times 17

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How to work it out

1
What is special about 53040: a Harshad number: divisible by its digit sum 12.
2
53040 is composite. Its prime factorisation is
$53040 = 2^{4} \times 3 \times 5 \times 13 \times 17$
3
The divisors add up to 187488; without 53040 itself that is 134448, so 53040 is abundant (134448 is more than 53040). Euler's totient φ(53040) = 12288 numbers up to 53040 share no factor with it.
4
The digits of 53040 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 78 steps to reach 1.

LaTeX source of the formulas on this page

\[ 53040 = 2^{4} \times 3 \times 5 \times 13 \times 17 \]

53040 at a glance

Property	Value
Type	composite
Number of divisors	80
Sum of divisors	187488
Euler totient φ(n)	12288
Square	2813241600
Cube	149214334464000
Square root	230.304147 (= 4√3315)
Digit sum / digital root	12 / 3
Collatz steps to 1	78
Scientific notation	5.304 × $10^{4}$

53040 in other forms

Form	Value
In words	fifty-three thousand and forty
Binary (base 2)	1100111100110000
Octal (base 8)	147460
Hexadecimal (base 16)	CF30
Base 3	2200202110
As time	53040 seconds = 14 h 44 min 0 s

Is 53040 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (53040 ÷ 2 = 26520)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (53040 ÷ 3 = 17680)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (53040 ÷ 4 = 13260)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (53040 ÷ 5 = 10608)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (53040 ÷ 6 = 8840)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 1)	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 (53040 ÷ 8 = 6630)	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 (53040 ÷ 10 = 5304)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 9)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (53040 ÷ 12 = 4420)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 53040 a prime number?

No. 53040 = $2^{4}$ × 3 × 5 × 13 × 17, so it is divisible by 2.

What are the factors of 53040?

1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 17, 20, 24, 26, 30, 34, 39, 40, 48, 51, 52, 60, 65, 68, 78, 80, 85, 102, 104, 120, 130, 136, 156, 170, 195, 204, 208, 221, 240, 255, 260, 272, 312, 340, 390, 408, 442, 510, 520, 624, 663, 680, 780, 816, 884, 1020, 1040, 1105, 1326, 1360, 1560, 1768, 2040, 2210, 2652, 3120, 3315, 3536, 4080, 4420, 5304, 6630, 8840, 10608, 13260, 17680, 26520, 53040.

What is 53040 in binary?

1100111100110000 (hexadecimal CF30, octal 147460).

What is the square root of 53040?

About 230.3041, exactly 4√3315.

Is 53040 divisible by 3?

Yes. Its digits add up to 12, a multiple of 3.

What is special about the number 53040?

53040 is a Harshad number: divisible by its digit sum 12.