The number 42504

Q: Is 42504 a prime number?

No. 42504 = 2^3 × 3 × 7 × 11 × 23, so it is divisible by 2.

42504 is a composite number with 64 divisors. Its prime factorisation is $2^{3}$ × 3 × 7 × 11 × 23. Divisors (64): 1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 21, 22, 23, 24, 28, 33 … 42504.

Number

Pick any whole number from 1 to 100,000.

42504 = 2^{3} \times 3 \times 7 \times 11 \times 23

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How to work it out

1
42504 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
42504 is composite. Its prime factorisation is
$42504 = 2^{3} \times 3 \times 7 \times 11 \times 23$
3
The divisors add up to 138240; without 42504 itself that is 95736, so 42504 is abundant (95736 is more than 42504). Euler's totient φ(42504) = 10560 numbers up to 42504 share no factor with it.
4
The digits of 42504 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 57 steps to reach 1.

LaTeX source of the formulas on this page

\[ 42504 = 2^{3} \times 3 \times 7 \times 11 \times 23 \]

42504 at a glance

Property	Value
Type	composite
Number of divisors	64
Sum of divisors	138240
Euler totient φ(n)	10560
Square	1806590016
Cube	76787302040064
Square root	206.164982 (= 2√10626)
Digit sum / digital root	15 / 6
Collatz steps to 1	57
Scientific notation	4.2504 × $10^{4}$

42504 in other forms

Form	Value
In words	forty-two thousand five hundred and four
Binary (base 2)	1010011000001000
Octal (base 8)	123010
Hexadecimal (base 16)	A608
Base 3	2011022020
As time	42504 seconds = 11 h 48 min 24 s

Is 42504 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (42504 ÷ 2 = 21252)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (42504 ÷ 3 = 14168)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (42504 ÷ 4 = 10626)	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 (42504 ÷ 6 = 7084)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (42504 ÷ 7 = 6072)	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 (42504 ÷ 8 = 5313)	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	No (remainder 4)	A number is divisible by 10 if the last digit is 0.
11	Yes (42504 ÷ 11 = 3864)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (42504 ÷ 12 = 3542)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 42504 a prime number?

No. 42504 = $2^{3}$ × 3 × 7 × 11 × 23, so it is divisible by 2.

What are the factors of 42504?

1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 21, 22, 23, 24, 28, 33, 42, 44, 46, 56, 66, 69, 77, 84, 88, 92, 132, 138, 154, 161, 168, 184, 231, 253, 264, 276, 308, 322, 462, 483, 506, 552, 616, 644, 759, 924, 966, 1012, 1288, 1518, 1771, 1848, 1932, 2024, 3036, 3542, 3864, 5313, 6072, 7084, 10626, 14168, 21252, 42504.

What is 42504 in binary?

1010011000001000 (hexadecimal A608, octal 123010).

What is the square root of 42504?

About 206.1650, exactly 2√10626.

Is 42504 divisible by 3?

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

What is special about the number 42504?

It is a composite number with 64 divisors.