The number 20460

Q: Is 20460 a prime number?

No. 20460 = 2^2 × 3 × 5 × 11 × 31, so it is divisible by 2.

20460 is a composite number with 48 divisors. Its prime factorisation is $2^{2}$ × 3 × 5 × 11 × 31. Divisors (48): 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 31, 33, 44 … 20460.

Number

Pick any whole number from 1 to 100,000.

20460 = 2^{2} \times 3 \times 5 \times 11 \times 31

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How to work it out

1
What is special about 20460: a Harshad number: divisible by its digit sum 12.
2
20460 is composite. Its prime factorisation is
$20460 = 2^{2} \times 3 \times 5 \times 11 \times 31$
3
The divisors add up to 64512; without 20460 itself that is 44052, so 20460 is abundant (44052 is more than 20460). Euler's totient φ(20460) = 4800 numbers up to 20460 share no factor with it.
4
The digits of 20460 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 61 steps to reach 1.

LaTeX source of the formulas on this page

\[ 20460 = 2^{2} \times 3 \times 5 \times 11 \times 31 \]

20460 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	64512
Euler totient φ(n)	4800
Square	418611600
Cube	8564793336000
Square root	143.038456 (= 2√5115)
Digit sum / digital root	12 / 3
Collatz steps to 1	61
Scientific notation	2.046 × $10^{4}$

20460 in other forms

Form	Value
In words	twenty thousand four hundred and sixty
Binary (base 2)	100111111101100
Octal (base 8)	47754
Hexadecimal (base 16)	4FEC
Base 3	1001001210
As time	20460 seconds = 5 h 41 min 0 s

Is 20460 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (20460 ÷ 2 = 10230)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (20460 ÷ 3 = 6820)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (20460 ÷ 4 = 5115)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (20460 ÷ 5 = 4092)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (20460 ÷ 6 = 3410)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 6)	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	Yes (20460 ÷ 10 = 2046)	A number is divisible by 10 if the last digit is 0.
11	Yes (20460 ÷ 11 = 1860)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (20460 ÷ 12 = 1705)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 20460 a prime number?

No. 20460 = $2^{2}$ × 3 × 5 × 11 × 31, so it is divisible by 2.

What are the factors of 20460?

1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 31, 33, 44, 55, 60, 62, 66, 93, 110, 124, 132, 155, 165, 186, 220, 310, 330, 341, 372, 465, 620, 660, 682, 930, 1023, 1364, 1705, 1860, 2046, 3410, 4092, 5115, 6820, 10230, 20460.

What is 20460 in binary?

100111111101100 (hexadecimal 4FEC, octal 47754).

What is the square root of 20460?

About 143.0385, exactly 2√5115.

Is 20460 divisible by 3?

Yes. Its digits add up to 12, a multiple of 3.

What is special about the number 20460?

20460 is a Harshad number: divisible by its digit sum 12.