The number 40560

Q: Is 40560 a prime number?

No. 40560 = 2^4 × 3 × 5 × 13^2, so it is divisible by 2.

40560 is a composite number with 60 divisors. Its prime factorisation is $2^{4}$ × 3 × 5 × $13^{2}$ . Divisors (60): 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 30 … 40560.

Number

Pick any whole number from 1 to 100,000.

40560 = 2^{4} \times 3 \times 5 \times 13^{2}

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How to work it out

1
What is special about 40560: a Harshad number: divisible by its digit sum 15.
2
40560 is composite. Its prime factorisation is
$40560 = 2^{4} \times 3 \times 5 \times 13^{2}$
3
The divisors add up to 136152; without 40560 itself that is 95592, so 40560 is abundant (95592 is more than 40560). Euler's totient φ(40560) = 9984 numbers up to 40560 share no factor with it.
4
The digits of 40560 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 88 steps to reach 1.

LaTeX source of the formulas on this page

\[ 40560 = 2^{4} \times 3 \times 5 \times 13^{2} \]

40560 at a glance

Property	Value
Type	composite
Number of divisors	60
Sum of divisors	136152
Euler totient φ(n)	9984
Square	1645113600
Cube	66725807616000
Square root	201.395134 (= 52√15)
Digit sum / digital root	15 / 6
Collatz steps to 1	88
Scientific notation	4.056 × $10^{4}$

40560 in other forms

Form	Value
In words	forty thousand five hundred and sixty
Binary (base 2)	1001111001110000
Octal (base 8)	117160
Hexadecimal (base 16)	9E70
Base 3	2001122020
As time	40560 seconds = 11 h 16 min 0 s

Is 40560 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (40560 ÷ 2 = 20280)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (40560 ÷ 3 = 13520)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (40560 ÷ 4 = 10140)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (40560 ÷ 5 = 8112)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (40560 ÷ 6 = 6760)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 2)	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 (40560 ÷ 8 = 5070)	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 (40560 ÷ 10 = 4056)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 3)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (40560 ÷ 12 = 3380)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 40560 a prime number?

No. 40560 = $2^{4}$ × 3 × 5 × $13^{2}$ , so it is divisible by 2.

What are the factors of 40560?

1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 30, 39, 40, 48, 52, 60, 65, 78, 80, 104, 120, 130, 156, 169, 195, 208, 240, 260, 312, 338, 390, 507, 520, 624, 676, 780, 845, 1014, 1040, 1352, 1560, 1690, 2028, 2535, 2704, 3120, 3380, 4056, 5070, 6760, 8112, 10140, 13520, 20280, 40560.

What is 40560 in binary?

1001111001110000 (hexadecimal 9E70, octal 117160).

What is the square root of 40560?

About 201.3951, exactly 52√15.

Is 40560 divisible by 3?

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

What is special about the number 40560?

40560 is a Harshad number: divisible by its digit sum 15.