The number 11760

Q: Is 11760 a prime number?

No. 11760 = 2^4 × 3 × 5 × 7^2, so it is divisible by 2.

11760 is a composite number with 60 divisors. Its prime factorisation is $2^{4}$ × 3 × 5 × $7^{2}$ . Divisors (60): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24 … 11760.

Number

Pick any whole number from 1 to 100,000.

11760 = 2^{4} \times 3 \times 5 \times 7^{2}

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How to work it out

1
What is special about 11760: a Harshad number: divisible by its digit sum 15.
2
11760 is composite. Its prime factorisation is
$11760 = 2^{4} \times 3 \times 5 \times 7^{2}$
3
The divisors add up to 42408; without 11760 itself that is 30648, so 11760 is abundant (30648 is more than 11760). Euler's totient φ(11760) = 2688 numbers up to 11760 share no factor with it.
4
The digits of 11760 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.

LaTeX source of the formulas on this page

\[ 11760 = 2^{4} \times 3 \times 5 \times 7^{2} \]

11760 at a glance

Property	Value
Type	composite
Number of divisors	60
Sum of divisors	42408
Euler totient φ(n)	2688
Square	138297600
Cube	1626379776000
Square root	108.443534 (= 28√15)
Digit sum / digital root	15 / 6
Collatz steps to 1	50
Scientific notation	1.176 × $10^{4}$

11760 in other forms

Form	Value
In words	eleven thousand seven hundred and sixty
Binary (base 2)	10110111110000
Octal (base 8)	26760
Hexadecimal (base 16)	2DF0
Base 3	121010120
As time	11760 seconds = 3 h 16 min 0 s

Is 11760 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (11760 ÷ 2 = 5880)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (11760 ÷ 3 = 3920)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (11760 ÷ 4 = 2940)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (11760 ÷ 5 = 2352)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (11760 ÷ 6 = 1960)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (11760 ÷ 7 = 1680)	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 (11760 ÷ 8 = 1470)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 6)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (11760 ÷ 10 = 1176)	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	Yes (11760 ÷ 12 = 980)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 11760 a prime number?

No. 11760 = $2^{4}$ × 3 × 5 × $7^{2}$ , so it is divisible by 2.

What are the factors of 11760?

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 49, 56, 60, 70, 80, 84, 98, 105, 112, 120, 140, 147, 168, 196, 210, 240, 245, 280, 294, 336, 392, 420, 490, 560, 588, 735, 784, 840, 980, 1176, 1470, 1680, 1960, 2352, 2940, 3920, 5880, 11760.

What is 11760 in binary?

10110111110000 (hexadecimal 2DF0, octal 26760).

What is the square root of 11760?

About 108.4435, exactly 28√15.

Is 11760 divisible by 3?

Yes. Its digits add up to 15, a multiple of 3.

What is special about the number 11760?

11760 is a Harshad number: divisible by its digit sum 15.