The number 45084

Q: Is 45084 a prime number?

No. 45084 = 2^2 × 3 × 13 × 17^2, so it is divisible by 2.

45084 is a composite number with 36 divisors. Its prime factorisation is $2^{2}$ × 3 × 13 × $17^{2}$ . Divisors (36): 1, 2, 3, 4, 6, 12, 13, 17, 26, 34, 39, 51, 52, 68, 78, 102 … 45084.

Number

Pick any whole number from 1 to 100,000.

45084 = 2^{2} \times 3 \times 13 \times 17^{2}

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How to work it out

1
45084 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
45084 is composite. Its prime factorisation is
$45084 = 2^{2} \times 3 \times 13 \times 17^{2}$
3
The divisors add up to 120344; without 45084 itself that is 75260, so 45084 is abundant (75260 is more than 45084). Euler's totient φ(45084) = 13056 numbers up to 45084 share no factor with it.
4
The digits of 45084 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 62 steps to reach 1.

LaTeX source of the formulas on this page

\[ 45084 = 2^{2} \times 3 \times 13 \times 17^{2} \]

45084 at a glance

Property	Value
Type	composite
Number of divisors	36
Sum of divisors	120344
Euler totient φ(n)	13056
Square	2032567056
Cube	91636253152704
Square root	212.329932 (= 34√39)
Digit sum / digital root	21 / 3
Collatz steps to 1	62
Scientific notation	4.5084 × $10^{4}$

45084 in other forms

Form	Value
In words	forty-five thousand and eighty-four
Binary (base 2)	1011000000011100
Octal (base 8)	130034
Hexadecimal (base 16)	B01C
Base 3	2021211210
As time	45084 seconds = 12 h 31 min 24 s

Is 45084 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (45084 ÷ 2 = 22542)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (45084 ÷ 3 = 15028)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (45084 ÷ 4 = 11271)	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 (45084 ÷ 6 = 7514)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 4)	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	No (remainder 4)	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	No (remainder 6)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (45084 ÷ 12 = 3757)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 45084 a prime number?

No. 45084 = $2^{2}$ × 3 × 13 × $17^{2}$ , so it is divisible by 2.

What are the factors of 45084?

1, 2, 3, 4, 6, 12, 13, 17, 26, 34, 39, 51, 52, 68, 78, 102, 156, 204, 221, 289, 442, 578, 663, 867, 884, 1156, 1326, 1734, 2652, 3468, 3757, 7514, 11271, 15028, 22542, 45084.

What is 45084 in binary?

1011000000011100 (hexadecimal B01C, octal 130034).

What is the square root of 45084?

About 212.3299, exactly 34√39.

Is 45084 divisible by 3?

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

What is special about the number 45084?

It is a composite number with 36 divisors.