The number 83028

Q: Is 83028 a prime number?

No. 83028 = 2^2 × 3 × 11 × 17 × 37, so it is divisible by 2.

83028 is a triangular number: 1 + 2 + … + 407 = 83028. Its prime factorisation is $2^{2}$ × 3 × 11 × 17 × 37. Divisors (48): 1, 2, 3, 4, 6, 11, 12, 17, 22, 33, 34, 37, 44, 51, 66, 68 … 83028.

Number

Pick any whole number from 1 to 100,000.

83028 = 2^{2} \times 3 \times 11 \times 17 \times 37

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How to work it out

1
What is special about 83028: a triangular number: 1 + 2 + … + 407 = 83028.
2
83028 is composite. Its prime factorisation is
$83028 = 2^{2} \times 3 \times 11 \times 17 \times 37$
3
The divisors add up to 229824; without 83028 itself that is 146796, so 83028 is abundant (146796 is more than 83028). Euler's totient φ(83028) = 23040 numbers up to 83028 share no factor with it.
4
The digits of 83028 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

\[ 83028 = 2^{2} \times 3 \times 11 \times 17 \times 37 \]

83028 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	229824
Euler totient φ(n)	23040
Square	6893648784
Cube	572365871237952
Square root	288.145796 (= 2√20757)
Digit sum / digital root	21 / 3
Collatz steps to 1	107
Scientific notation	8.3028 × $10^{4}$

83028 in other forms

Form	Value
In words	eighty-three thousand and twenty-eight
Binary (base 2)	10100010001010100
Octal (base 8)	242124
Hexadecimal (base 16)	14454
Base 3	11012220010
As time	83028 seconds = 23 h 3 min 48 s

Is 83028 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (83028 ÷ 2 = 41514)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (83028 ÷ 3 = 27676)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (83028 ÷ 4 = 20757)	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 (83028 ÷ 6 = 13838)	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	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 8)	A number is divisible by 10 if the last digit is 0.
11	Yes (83028 ÷ 11 = 7548)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (83028 ÷ 12 = 6919)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 83028 a prime number?

No. 83028 = $2^{2}$ × 3 × 11 × 17 × 37, so it is divisible by 2.

What are the factors of 83028?

1, 2, 3, 4, 6, 11, 12, 17, 22, 33, 34, 37, 44, 51, 66, 68, 74, 102, 111, 132, 148, 187, 204, 222, 374, 407, 444, 561, 629, 748, 814, 1122, 1221, 1258, 1628, 1887, 2244, 2442, 2516, 3774, 4884, 6919, 7548, 13838, 20757, 27676, 41514, 83028.

What is 83028 in binary?

10100010001010100 (hexadecimal 14454, octal 242124).

What is the square root of 83028?

About 288.1458, exactly 2√20757.

Is 83028 divisible by 3?

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

What is special about the number 83028?

83028 is a triangular number: 1 + 2 + … + 407 = 83028.