The number 77880

Q: Is 77880 a prime number?

No. 77880 = 2^3 × 3 × 5 × 11 × 59, so it is divisible by 2.

77880 is a composite number with 64 divisors. Its prime factorisation is $2^{3}$ × 3 × 5 × 11 × 59. Divisors (64): 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 30, 33 … 77880.

Number

Pick any whole number from 1 to 100,000.

77880 = 2^{3} \times 3 \times 5 \times 11 \times 59

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How to work it out

1
What is special about 77880: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 30.
2
77880 is composite. Its prime factorisation is
$77880 = 2^{3} \times 3 \times 5 \times 11 \times 59$
3
The divisors add up to 259200; without 77880 itself that is 181320, so 77880 is abundant (181320 is more than 77880). Euler's totient φ(77880) = 18560 numbers up to 77880 share no factor with it.
4
The digits of 77880 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.

LaTeX source of the formulas on this page

\[ 77880 = 2^{3} \times 3 \times 5 \times 11 \times 59 \]

77880 at a glance

Property	Value
Type	composite
Number of divisors	64
Sum of divisors	259200
Euler totient φ(n)	18560
Square	6065294400
Cube	472365127872000
Square root	279.069884 (= 2√19470)
Digit sum / digital root	30 / 3
Collatz steps to 1	50
Scientific notation	7.788 × $10^{4}$

77880 in other forms

Form	Value
In words	seventy-seven thousand eight hundred and eighty
Binary (base 2)	10011000000111000
Octal (base 8)	230070
Hexadecimal (base 16)	13038
Base 3	10221211110
As time	77880 seconds = 21 h 38 min 0 s

Is 77880 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (77880 ÷ 2 = 38940)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (77880 ÷ 3 = 25960)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (77880 ÷ 4 = 19470)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (77880 ÷ 5 = 15576)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (77880 ÷ 6 = 12980)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 5)	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 (77880 ÷ 8 = 9735)	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 (77880 ÷ 10 = 7788)	A number is divisible by 10 if the last digit is 0.
11	Yes (77880 ÷ 11 = 7080)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (77880 ÷ 12 = 6490)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 77880 a prime number?

No. 77880 = $2^{3}$ × 3 × 5 × 11 × 59, so it is divisible by 2.

What are the factors of 77880?

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 30, 33, 40, 44, 55, 59, 60, 66, 88, 110, 118, 120, 132, 165, 177, 220, 236, 264, 295, 330, 354, 440, 472, 590, 649, 660, 708, 885, 1180, 1298, 1320, 1416, 1770, 1947, 2360, 2596, 3245, 3540, 3894, 5192, 6490, 7080, 7788, 9735, 12980, 15576, 19470, 25960, 38940, 77880.

What is 77880 in binary?

10011000000111000 (hexadecimal 13038, octal 230070).

What is the square root of 77880?

About 279.0699, exactly 2√19470.

Is 77880 divisible by 3?

Yes. Its digits add up to 30, a multiple of 3.

What is special about the number 77880?

77880 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 30.