The number 35280

Q: Is 35280 a prime number?

No. 35280 = 2^4 × 3^2 × 5 × 7^2, so it is divisible by 2.

35280 is a composite number with 90 divisors. Its prime factorisation is $2^{4}$ × $3^{2}$ × 5 × $7^{2}$ . Divisors (90): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20 … 35280.

Number

Pick any whole number from 1 to 100,000.

35280 = 2^{4} \times 3^{2} \times 5 \times 7^{2}

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How to work it out

1
What is special about 35280: a Harshad number: divisible by its digit sum 18.
2
35280 is composite. Its prime factorisation is
$35280 = 2^{4} \times 3^{2} \times 5 \times 7^{2}$
3
The divisors add up to 137826; without 35280 itself that is 102546, so 35280 is abundant (102546 is more than 35280). Euler's totient φ(35280) = 8064 numbers up to 35280 share no factor with it.
4
The digits of 35280 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 49 steps to reach 1.

LaTeX source of the formulas on this page

\[ 35280 = 2^{4} \times 3^{2} \times 5 \times 7^{2} \]

35280 at a glance

Property	Value
Type	composite
Number of divisors	90
Sum of divisors	137826
Euler totient φ(n)	8064
Square	1244678400
Cube	43912253952000
Square root	187.829710 (= 84√5)
Digit sum / digital root	18 / 9
Collatz steps to 1	49
Scientific notation	3.528 × $10^{4}$

35280 in other forms

Form	Value
In words	thirty-five thousand two hundred and eighty
Binary (base 2)	1000100111010000
Octal (base 8)	104720
Hexadecimal (base 16)	89D0
Base 3	1210101200
As time	35280 seconds = 9 h 48 min 0 s

Is 35280 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (35280 ÷ 2 = 17640)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (35280 ÷ 3 = 11760)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (35280 ÷ 4 = 8820)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (35280 ÷ 5 = 7056)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (35280 ÷ 6 = 5880)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (35280 ÷ 7 = 5040)	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 (35280 ÷ 8 = 4410)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (35280 ÷ 9 = 3920)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (35280 ÷ 10 = 3528)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 3)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (35280 ÷ 12 = 2940)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 35280 a prime number?

No. 35280 = $2^{4}$ × $3^{2}$ × 5 × $7^{2}$ , so it is divisible by 2.

What are the factors of 35280?

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 49, 56, 60, 63, 70, 72, 80, 84, 90, 98, 105, 112, 120, 126, 140, 144, 147, 168, 180, 196, 210, 240, 245, 252, 280, 294, 315, 336, 360, 392, 420, 441, 490, 504, 560, 588, 630, 720, 735, 784, 840, 882, 980, 1008, 1176, 1260, 1470, 1680, 1764, 1960, 2205, 2352, 2520, 2940, 3528, 3920, 4410, 5040, 5880, 7056, 8820, 11760, 17640, 35280.

What is 35280 in binary?

1000100111010000 (hexadecimal 89D0, octal 104720).

What is the square root of 35280?

About 187.8297, exactly 84√5.

Is 35280 divisible by 3?

Yes. Its digits add up to 18, a multiple of 3.

What is special about the number 35280?

35280 is a Harshad number: divisible by its digit sum 18.