The number 76800

Q: Is 76800 a prime number?

No. 76800 = 2^10 × 3 × 5^2, so it is divisible by 2.

76800 is a composite number with 66 divisors. Its prime factorisation is $2^{10}$ × 3 × $5^{2}$ . Divisors (66): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32 … 76800.

Number

Pick any whole number from 1 to 100,000.

76800 = 2^{10} \times 3 \times 5^{2}

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How to work it out

1
76800 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
76800 is composite. Its prime factorisation is
$76800 = 2^{10} \times 3 \times 5^{2}$
3
The divisors add up to 253828; without 76800 itself that is 177028, so 76800 is abundant (177028 is more than 76800). Euler's totient φ(76800) = 20480 numbers up to 76800 share no factor with it.
4
The digits of 76800 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 24 steps to reach 1.

LaTeX source of the formulas on this page

\[ 76800 = 2^{10} \times 3 \times 5^{2} \]

76800 at a glance

Property	Value
Type	composite
Number of divisors	66
Sum of divisors	253828
Euler totient φ(n)	20480
Square	5898240000
Cube	452984832000000
Square root	277.128129 (= 160√3)
Digit sum / digital root	21 / 3
Collatz steps to 1	24
Scientific notation	7.68 × $10^{4}$

76800 in other forms

Form	Value
In words	seventy-six thousand eight hundred
Binary (base 2)	10010110000000000
Octal (base 8)	226000
Hexadecimal (base 16)	12C00
Base 3	10220100110
As time	76800 seconds = 21 h 20 min 0 s

Is 76800 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (76800 ÷ 2 = 38400)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (76800 ÷ 3 = 25600)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (76800 ÷ 4 = 19200)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (76800 ÷ 5 = 15360)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (76800 ÷ 6 = 12800)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 3)	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 (76800 ÷ 8 = 9600)	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 (76800 ÷ 10 = 7680)	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 (76800 ÷ 12 = 6400)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 76800 a prime number?

No. 76800 = $2^{10}$ × 3 × $5^{2}$ , so it is divisible by 2.

What are the factors of 76800?

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 256, 300, 320, 384, 400, 480, 512, 600, 640, 768, 800, 960, 1024, 1200, 1280, 1536, 1600, 1920, 2400, 2560, 3072, 3200, 3840, 4800, 5120, 6400, 7680, 9600, 12800, 15360, 19200, 25600, 38400, 76800.

What is 76800 in binary?

10010110000000000 (hexadecimal 12C00, octal 226000).

What is the square root of 76800?

About 277.1281, exactly 160√3.

Is 76800 divisible by 3?

Yes. Its digits add up to 21, a multiple of 3.

What is special about the number 76800?

It is a composite number with 66 divisors.