The number 47040

Q: Is 47040 a prime number?

No. 47040 = 2^6 × 3 × 5 × 7^2, so it is divisible by 2.

47040 is a composite number with 84 divisors. Its prime factorisation is $2^{6}$ × 3 × 5 × $7^{2}$ . Divisors (84): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24 … 47040.

Number

Pick any whole number from 1 to 100,000.

47040 = 2^{6} \times 3 \times 5 \times 7^{2}

Explain it step by step in chat Make a short video of it

How to work it out

1
What is special about 47040: a Harshad number: divisible by its digit sum 15.
2
47040 is composite. Its prime factorisation is
$47040 = 2^{6} \times 3 \times 5 \times 7^{2}$
3
The divisors add up to 173736; without 47040 itself that is 126696, so 47040 is abundant (126696 is more than 47040). Euler's totient φ(47040) = 10752 numbers up to 47040 share no factor with it.
4
The digits of 47040 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 52 steps to reach 1.

LaTeX source of the formulas on this page

\[ 47040 = 2^{6} \times 3 \times 5 \times 7^{2} \]

47040 at a glance

Property	Value
Type	composite
Number of divisors	84
Sum of divisors	173736
Euler totient φ(n)	10752
Square	2212761600
Cube	104088305664000
Square root	216.887067 (= 56√15)
Digit sum / digital root	15 / 6
Collatz steps to 1	52
Scientific notation	4.704 × $10^{4}$

47040 in other forms

Form	Value
In words	forty-seven thousand and forty
Binary (base 2)	1011011111000000
Octal (base 8)	133700
Hexadecimal (base 16)	B7C0
Base 3	2101112020
As time	47040 seconds = 13 h 4 min 0 s

Is 47040 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (47040 ÷ 2 = 23520)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (47040 ÷ 3 = 15680)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (47040 ÷ 4 = 11760)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (47040 ÷ 5 = 9408)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (47040 ÷ 6 = 7840)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (47040 ÷ 7 = 6720)	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 (47040 ÷ 8 = 5880)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 6)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (47040 ÷ 10 = 4704)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 4)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (47040 ÷ 12 = 3920)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 47040 a prime number?

No. 47040 = $2^{6}$ × 3 × 5 × $7^{2}$ , so it is divisible by 2.

What are the factors of 47040?

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 49, 56, 60, 64, 70, 80, 84, 96, 98, 105, 112, 120, 140, 147, 160, 168, 192, 196, 210, 224, 240, 245, 280, 294, 320, 336, 392, 420, 448, 480, 490, 560, 588, 672, 735, 784, 840, 960, 980, 1120, 1176, 1344, 1470, 1568, 1680, 1960, 2240, 2352, 2940, 3136, 3360, 3920, 4704, 5880, 6720, 7840, 9408, 11760, 15680, 23520, 47040.

What is 47040 in binary?

1011011111000000 (hexadecimal B7C0, octal 133700).

What is the square root of 47040?

About 216.8871, exactly 56√15.

Is 47040 divisible by 3?

Yes. Its digits add up to 15, a multiple of 3.

What is special about the number 47040?

47040 is a Harshad number: divisible by its digit sum 15.