The number 75504

Q: Is 75504 a prime number?

No. 75504 = 2^4 × 3 × 11^2 × 13, so it is divisible by 2.

75504 is a composite number with 60 divisors. Its prime factorisation is $2^{4}$ × 3 × $11^{2}$ × 13. Divisors (60): 1, 2, 3, 4, 6, 8, 11, 12, 13, 16, 22, 24, 26, 33, 39, 44 … 75504.

Number

Pick any whole number from 1 to 100,000.

75504 = 2^{4} \times 3 \times 11^{2} \times 13

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How to work it out

1
75504 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
75504 is composite. Its prime factorisation is
$75504 = 2^{4} \times 3 \times 11^{2} \times 13$
3
The divisors add up to 230888; without 75504 itself that is 155384, so 75504 is abundant (155384 is more than 75504). Euler's totient φ(75504) = 21120 numbers up to 75504 share no factor with it.
4
The digits of 75504 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 107 steps to reach 1.

LaTeX source of the formulas on this page

\[ 75504 = 2^{4} \times 3 \times 11^{2} \times 13 \]

75504 at a glance

Property	Value
Type	composite
Number of divisors	60
Sum of divisors	230888
Euler totient φ(n)	21120
Square	5700854016
Cube	430437281624064
Square root	274.779912 (= 44√39)
Digit sum / digital root	21 / 3
Collatz steps to 1	107
Scientific notation	7.5504 × $10^{4}$

75504 in other forms

Form	Value
In words	seventy-five thousand five hundred and four
Binary (base 2)	10010011011110000
Octal (base 8)	223360
Hexadecimal (base 16)	126F0
Base 3	10211120110
As time	75504 seconds = 20 h 58 min 24 s

Is 75504 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (75504 ÷ 2 = 37752)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (75504 ÷ 3 = 25168)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (75504 ÷ 4 = 18876)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 4)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (75504 ÷ 6 = 12584)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 2)	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 (75504 ÷ 8 = 9438)	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	No (remainder 4)	A number is divisible by 10 if the last digit is 0.
11	Yes (75504 ÷ 11 = 6864)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (75504 ÷ 12 = 6292)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 75504 a prime number?

No. 75504 = $2^{4}$ × 3 × $11^{2}$ × 13, so it is divisible by 2.

What are the factors of 75504?

1, 2, 3, 4, 6, 8, 11, 12, 13, 16, 22, 24, 26, 33, 39, 44, 48, 52, 66, 78, 88, 104, 121, 132, 143, 156, 176, 208, 242, 264, 286, 312, 363, 429, 484, 528, 572, 624, 726, 858, 968, 1144, 1452, 1573, 1716, 1936, 2288, 2904, 3146, 3432, 4719, 5808, 6292, 6864, 9438, 12584, 18876, 25168, 37752, 75504.

What is 75504 in binary?

10010011011110000 (hexadecimal 126F0, octal 223360).

What is the square root of 75504?

About 274.7799, exactly 44√39.

Is 75504 divisible by 3?

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

What is special about the number 75504?

It is a composite number with 60 divisors.