The number 90168

Q: Is 90168 a prime number?

No. 90168 = 2^3 × 3 × 13 × 17^2, so it is divisible by 2.

90168 is a composite number with 48 divisors. Its prime factorisation is $2^{3}$ × 3 × 13 × $17^{2}$ . Divisors (48): 1, 2, 3, 4, 6, 8, 12, 13, 17, 24, 26, 34, 39, 51, 52, 68 … 90168.

Number

Pick any whole number from 1 to 100,000.

90168 = 2^{3} \times 3 \times 13 \times 17^{2}

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How to work it out

1
What is special about 90168: a Harshad number: divisible by its digit sum 24.
2
90168 is composite. Its prime factorisation is
$90168 = 2^{3} \times 3 \times 13 \times 17^{2}$
3
The divisors add up to 257880; without 90168 itself that is 167712, so 90168 is abundant (167712 is more than 90168). Euler's totient φ(90168) = 26112 numbers up to 90168 share no factor with it.
4
The digits of 90168 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 63 steps to reach 1.

LaTeX source of the formulas on this page

\[ 90168 = 2^{3} \times 3 \times 13 \times 17^{2} \]

90168 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	257880
Euler totient φ(n)	26112
Square	8130268224
Cube	733090025221632
Square root	300.279869 (= 34√78)
Digit sum / digital root	24 / 6
Collatz steps to 1	63
Scientific notation	9.0168 × $10^{4}$

90168 in other forms

Form	Value
In words	ninety thousand one hundred and sixty-eight
Binary (base 2)	10110000000111000
Octal (base 8)	260070
Hexadecimal (base 16)	16038
Base 3	11120200120
As time	90168 seconds = 25 h 2 min 48 s

Is 90168 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (90168 ÷ 2 = 45084)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (90168 ÷ 3 = 30056)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (90168 ÷ 4 = 22542)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 3)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (90168 ÷ 6 = 15028)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 1)	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 (90168 ÷ 8 = 11271)	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 8)	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 (90168 ÷ 12 = 7514)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 90168 a prime number?

No. 90168 = $2^{3}$ × 3 × 13 × $17^{2}$ , so it is divisible by 2.

What are the factors of 90168?

1, 2, 3, 4, 6, 8, 12, 13, 17, 24, 26, 34, 39, 51, 52, 68, 78, 102, 104, 136, 156, 204, 221, 289, 312, 408, 442, 578, 663, 867, 884, 1156, 1326, 1734, 1768, 2312, 2652, 3468, 3757, 5304, 6936, 7514, 11271, 15028, 22542, 30056, 45084, 90168.

What is 90168 in binary?

10110000000111000 (hexadecimal 16038, octal 260070).

What is the square root of 90168?

About 300.2799, exactly 34√78.

Is 90168 divisible by 3?

Yes. Its digits add up to 24, a multiple of 3.

What is special about the number 90168?

90168 is a Harshad number: divisible by its digit sum 24.