The number 33800

Q: Is 33800 a prime number?

No. 33800 = 2^3 × 5^2 × 13^2, so it is divisible by 2.

33800 is a composite number with 36 divisors. Its prime factorisation is $2^{3}$ × $5^{2}$ × $13^{2}$ . Divisors (36): 1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104 … 33800.

Number

Pick any whole number from 1 to 100,000.

33800 = 2^{3} \times 5^{2} \times 13^{2}

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How to work it out

1
What is special about 33800: a happy number: repeatedly adding the squares of its digits reaches 1.
2
33800 is composite. Its prime factorisation is
$33800 = 2^{3} \times 5^{2} \times 13^{2}$
3
The divisors add up to 85095; without 33800 itself that is 51295, so 33800 is abundant (51295 is more than 33800). Euler's totient φ(33800) = 12480 numbers up to 33800 share no factor with it.
4
The digits of 33800 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 59 steps to reach 1.

LaTeX source of the formulas on this page

\[ 33800 = 2^{3} \times 5^{2} \times 13^{2} \]

33800 at a glance

Property	Value
Type	composite
Number of divisors	36
Sum of divisors	85095
Euler totient φ(n)	12480
Square	1142440000
Cube	38614472000000
Square root	183.847763 (= 130√2)
Digit sum / digital root	14 / 5
Collatz steps to 1	59
Scientific notation	3.38 × $10^{4}$

33800 in other forms

Form	Value
In words	thirty-three thousand eight hundred
Binary (base 2)	1000010000001000
Octal (base 8)	102010
Hexadecimal (base 16)	8408
Base 3	1201100212
As time	33800 seconds = 9 h 23 min 20 s

Is 33800 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (33800 ÷ 2 = 16900)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	No (remainder 2)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (33800 ÷ 4 = 8450)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (33800 ÷ 5 = 6760)	A number is divisible by 5 if the last digit is 0 or 5.
6	No (remainder 2)	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	Yes (33800 ÷ 8 = 4225)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 5)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (33800 ÷ 10 = 3380)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 8)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	No (remainder 8)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 33800 a prime number?

No. 33800 = $2^{3}$ × $5^{2}$ × $13^{2}$ , so it is divisible by 2.

What are the factors of 33800?

1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 130, 169, 200, 260, 325, 338, 520, 650, 676, 845, 1300, 1352, 1690, 2600, 3380, 4225, 6760, 8450, 16900, 33800.

What is 33800 in binary?

1000010000001000 (hexadecimal 8408, octal 102010).

What is the square root of 33800?

About 183.8478, exactly 130√2.

Is 33800 divisible by 3?

No. Its digits add up to 14, which is not a multiple of 3.

What is special about the number 33800?

33800 is a happy number: repeatedly adding the squares of its digits reaches 1.