The number 17640

Q: Is 17640 a prime number?

No. 17640 = 2^3 × 3^2 × 5 × 7^2, so it is divisible by 2.

17640 is a composite number with 72 divisors. Its prime factorisation is $2^{3}$ × $3^{2}$ × 5 × $7^{2}$ . Divisors (72): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21 … 17640.

Number

Pick any whole number from 1 to 100,000.

17640 = 2^{3} \times 3^{2} \times 5 \times 7^{2}

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How to work it out

1
What is special about 17640: a Harshad number: divisible by its digit sum 18.
2
17640 is composite. Its prime factorisation is
$17640 = 2^{3} \times 3^{2} \times 5 \times 7^{2}$
3
The divisors add up to 66690; without 17640 itself that is 49050, so 17640 is abundant (49050 is more than 17640). Euler's totient φ(17640) = 4032 numbers up to 17640 share no factor with it.
4
The digits of 17640 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 48 steps to reach 1.

LaTeX source of the formulas on this page

\[ 17640 = 2^{3} \times 3^{2} \times 5 \times 7^{2} \]

17640 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	66690
Euler totient φ(n)	4032
Square	311169600
Cube	5489031744000
Square root	132.815662 (= 42√10)
Digit sum / digital root	18 / 9
Collatz steps to 1	48
Scientific notation	1.764 × $10^{4}$

17640 in other forms

Form	Value
In words	seventeen thousand six hundred and forty
Binary (base 2)	100010011101000
Octal (base 8)	42350
Hexadecimal (base 16)	44E8
Base 3	220012100
As time	17640 seconds = 4 h 54 min 0 s

Is 17640 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (17640 ÷ 2 = 8820)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (17640 ÷ 3 = 5880)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (17640 ÷ 4 = 4410)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (17640 ÷ 5 = 3528)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (17640 ÷ 6 = 2940)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (17640 ÷ 7 = 2520)	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 (17640 ÷ 8 = 2205)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (17640 ÷ 9 = 1960)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (17640 ÷ 10 = 1764)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 7)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (17640 ÷ 12 = 1470)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 17640 a prime number?

No. 17640 = $2^{3}$ × $3^{2}$ × 5 × $7^{2}$ , so it is divisible by 2.

What are the factors of 17640?

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

What is 17640 in binary?

100010011101000 (hexadecimal 44E8, octal 42350).

What is the square root of 17640?

About 132.8157, exactly 42√10.

Is 17640 divisible by 3?

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

What is special about the number 17640?

17640 is a Harshad number: divisible by its digit sum 18.