The number 46020

Q: Is 46020 a prime number?

No. 46020 = 2^2 × 3 × 5 × 13 × 59, so it is divisible by 2.

46020 is a composite number with 48 divisors. Its prime factorisation is $2^{2}$ × 3 × 5 × 13 × 59. Divisors (48): 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 59 … 46020.

Number

Pick any whole number from 1 to 100,000.

46020 = 2^{2} \times 3 \times 5 \times 13 \times 59

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How to work it out

1
What is special about 46020: a Harshad number: divisible by its digit sum 12.
2
46020 is composite. Its prime factorisation is
$46020 = 2^{2} \times 3 \times 5 \times 13 \times 59$
3
The divisors add up to 141120; without 46020 itself that is 95100, so 46020 is abundant (95100 is more than 46020). Euler's totient φ(46020) = 11136 numbers up to 46020 share no factor with it.
4
The digits of 46020 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 57 steps to reach 1.

LaTeX source of the formulas on this page

\[ 46020 = 2^{2} \times 3 \times 5 \times 13 \times 59 \]

46020 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	141120
Euler totient φ(n)	11136
Square	2117840400
Cube	97463015208000
Square root	214.522726 (= 2√11505)
Digit sum / digital root	12 / 3
Collatz steps to 1	57
Scientific notation	4.602 × $10^{4}$

46020 in other forms

Form	Value
In words	forty-six thousand and twenty
Binary (base 2)	1011001111000100
Octal (base 8)	131704
Hexadecimal (base 16)	B3C4
Base 3	2100010110
As time	46020 seconds = 12 h 47 min 0 s

Is 46020 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (46020 ÷ 2 = 23010)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (46020 ÷ 3 = 15340)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (46020 ÷ 4 = 11505)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (46020 ÷ 5 = 9204)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (46020 ÷ 6 = 7670)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 2)	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 (46020 ÷ 10 = 4602)	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 (46020 ÷ 12 = 3835)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 46020 a prime number?

No. 46020 = $2^{2}$ × 3 × 5 × 13 × 59, so it is divisible by 2.

What are the factors of 46020?

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 59, 60, 65, 78, 118, 130, 156, 177, 195, 236, 260, 295, 354, 390, 590, 708, 767, 780, 885, 1180, 1534, 1770, 2301, 3068, 3540, 3835, 4602, 7670, 9204, 11505, 15340, 23010, 46020.

What is 46020 in binary?

1011001111000100 (hexadecimal B3C4, octal 131704).

What is the square root of 46020?

About 214.5227, exactly 2√11505.

Is 46020 divisible by 3?

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

What is special about the number 46020?

46020 is a Harshad number: divisible by its digit sum 12.