The number 67760

Q: Is 67760 a prime number?

No. 67760 = 2^4 × 5 × 7 × 11^2, so it is divisible by 2.

67760 is a composite number with 60 divisors. Its prime factorisation is $2^{4}$ × 5 × 7 × $11^{2}$ . Divisors (60): 1, 2, 4, 5, 7, 8, 10, 11, 14, 16, 20, 22, 28, 35, 40, 44 … 67760.

Number

Pick any whole number from 1 to 100,000.

67760 = 2^{4} \times 5 \times 7 \times 11^{2}

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How to work it out

1
67760 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
67760 is composite. Its prime factorisation is
$67760 = 2^{4} \times 5 \times 7 \times 11^{2}$
3
The divisors add up to 197904; without 67760 itself that is 130144, so 67760 is abundant (130144 is more than 67760). Euler's totient φ(67760) = 21120 numbers up to 67760 share no factor with it.
4
The digits of 67760 add up to 26, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 60 steps to reach 1.

LaTeX source of the formulas on this page

\[ 67760 = 2^{4} \times 5 \times 7 \times 11^{2} \]

67760 at a glance

Property	Value
Type	composite
Number of divisors	60
Sum of divisors	197904
Euler totient φ(n)	21120
Square	4591417600
Cube	311114456576000
Square root	260.307510 (= 44√35)
Digit sum / digital root	26 / 8
Collatz steps to 1	60
Scientific notation	6.776 × $10^{4}$

67760 in other forms

Form	Value
In words	sixty-seven thousand seven hundred and sixty
Binary (base 2)	10000100010110000
Octal (base 8)	204260
Hexadecimal (base 16)	108B0
Base 3	10102221122
As time	67760 seconds = 18 h 49 min 20 s

Is 67760 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (67760 ÷ 2 = 33880)	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 (67760 ÷ 4 = 16940)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (67760 ÷ 5 = 13552)	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	Yes (67760 ÷ 7 = 9680)	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 (67760 ÷ 8 = 8470)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 8)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (67760 ÷ 10 = 6776)	A number is divisible by 10 if the last digit is 0.
11	Yes (67760 ÷ 11 = 6160)	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 67760 a prime number?

No. 67760 = $2^{4}$ × 5 × 7 × $11^{2}$ , so it is divisible by 2.

What are the factors of 67760?

1, 2, 4, 5, 7, 8, 10, 11, 14, 16, 20, 22, 28, 35, 40, 44, 55, 56, 70, 77, 80, 88, 110, 112, 121, 140, 154, 176, 220, 242, 280, 308, 385, 440, 484, 560, 605, 616, 770, 847, 880, 968, 1210, 1232, 1540, 1694, 1936, 2420, 3080, 3388, 4235, 4840, 6160, 6776, 8470, 9680, 13552, 16940, 33880, 67760.

What is 67760 in binary?

10000100010110000 (hexadecimal 108B0, octal 204260).

What is the square root of 67760?

About 260.3075, exactly 44√35.

Is 67760 divisible by 3?

No. Its digits add up to 26, which is not a multiple of 3.

What is special about the number 67760?

It is a composite number with 60 divisors.