The number 81120

Q: Is 81120 a prime number?

No. 81120 = 2^5 × 3 × 5 × 13^2, so it is divisible by 2.

81120 is a composite number with 72 divisors. Its prime factorisation is $2^{5}$ × 3 × 5 × $13^{2}$ . Divisors (72): 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 30 … 81120.

Number

Pick any whole number from 1 to 100,000.

81120 = 2^{5} \times 3 \times 5 \times 13^{2}

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

How to work it out

1
What is special about 81120: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.
2
81120 is composite. Its prime factorisation is
$81120 = 2^{5} \times 3 \times 5 \times 13^{2}$
3
The divisors add up to 276696; without 81120 itself that is 195576, so 81120 is abundant (195576 is more than 81120). Euler's totient φ(81120) = 19968 numbers up to 81120 share no factor with it.
4
The digits of 81120 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 89 steps to reach 1.

LaTeX source of the formulas on this page

\[ 81120 = 2^{5} \times 3 \times 5 \times 13^{2} \]

81120 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	276696
Euler totient φ(n)	19968
Square	6580454400
Cube	533806460928000
Square root	284.815730 (= 52√30)
Digit sum / digital root	12 / 3
Collatz steps to 1	89
Scientific notation	8.112 × $10^{4}$

81120 in other forms

Form	Value
In words	eighty-one thousand one hundred and twenty
Binary (base 2)	10011110011100000
Octal (base 8)	236340
Hexadecimal (base 16)	13CE0
Base 3	11010021110
As time	81120 seconds = 22 h 32 min 0 s

Is 81120 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (81120 ÷ 2 = 40560)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (81120 ÷ 3 = 27040)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (81120 ÷ 4 = 20280)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (81120 ÷ 5 = 16224)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (81120 ÷ 6 = 13520)	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	Yes (81120 ÷ 8 = 10140)	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 (81120 ÷ 10 = 8112)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 6)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (81120 ÷ 12 = 6760)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 81120 a prime number?

No. 81120 = $2^{5}$ × 3 × 5 × $13^{2}$ , so it is divisible by 2.

What are the factors of 81120?

1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 30, 32, 39, 40, 48, 52, 60, 65, 78, 80, 96, 104, 120, 130, 156, 160, 169, 195, 208, 240, 260, 312, 338, 390, 416, 480, 507, 520, 624, 676, 780, 845, 1014, 1040, 1248, 1352, 1560, 1690, 2028, 2080, 2535, 2704, 3120, 3380, 4056, 5070, 5408, 6240, 6760, 8112, 10140, 13520, 16224, 20280, 27040, 40560, 81120.

What is 81120 in binary?

10011110011100000 (hexadecimal 13CE0, octal 236340).

What is the square root of 81120?

About 284.8157, exactly 52√30.

Is 81120 divisible by 3?

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

What is special about the number 81120?

81120 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.