The number 76880

Q: Is 76880 a prime number?

No. 76880 = 2^4 × 5 × 31^2, so it is divisible by 2.

76880 is a composite number with 30 divisors. Its prime factorisation is $2^{4}$ × 5 × $31^{2}$ . Divisors (30): 1, 2, 4, 5, 8, 10, 16, 20, 31, 40, 62, 80, 124, 155, 248, 310 … 76880.

Number

Pick any whole number from 1 to 100,000.

76880 = 2^{4} \times 5 \times 31^{2}

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How to work it out

1
76880 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
76880 is composite. Its prime factorisation is
$76880 = 2^{4} \times 5 \times 31^{2}$
3
The divisors add up to 184698; without 76880 itself that is 107818, so 76880 is abundant (107818 is more than 76880). Euler's totient φ(76880) = 29760 numbers up to 76880 share no factor with it.
4
The digits of 76880 add up to 29, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 63 steps to reach 1.

LaTeX source of the formulas on this page

\[ 76880 = 2^{4} \times 5 \times 31^{2} \]

76880 at a glance

Property	Value
Type	composite
Number of divisors	30
Sum of divisors	184698
Euler totient φ(n)	29760
Square	5910534400
Cube	454401884672000
Square root	277.272429 (= 124√5)
Digit sum / digital root	29 / 2
Collatz steps to 1	63
Scientific notation	7.688 × $10^{4}$

76880 in other forms

Form	Value
In words	seventy-six thousand eight hundred and eighty
Binary (base 2)	10010110001010000
Octal (base 8)	226120
Hexadecimal (base 16)	12C50
Base 3	10220110102
As time	76880 seconds = 21 h 21 min 20 s

Is 76880 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (76880 ÷ 2 = 38440)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	No (remainder 2)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (76880 ÷ 4 = 19220)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (76880 ÷ 5 = 15376)	A number is divisible by 5 if the last digit is 0 or 5.
6	No (remainder 2)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 6)	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 (76880 ÷ 8 = 9610)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 2)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (76880 ÷ 10 = 7688)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 1)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	No (remainder 8)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 76880 a prime number?

No. 76880 = $2^{4}$ × 5 × $31^{2}$ , so it is divisible by 2.

What are the factors of 76880?

1, 2, 4, 5, 8, 10, 16, 20, 31, 40, 62, 80, 124, 155, 248, 310, 496, 620, 961, 1240, 1922, 2480, 3844, 4805, 7688, 9610, 15376, 19220, 38440, 76880.

What is 76880 in binary?

10010110001010000 (hexadecimal 12C50, octal 226120).

What is the square root of 76880?

About 277.2724, exactly 124√5.

Is 76880 divisible by 3?

No. Its digits add up to 29, which is not a multiple of 3.

What is special about the number 76880?

It is a composite number with 30 divisors.