The number 46200

Q: Is 46200 a prime number?

No. 46200 = 2^3 × 3 × 5^2 × 7 × 11, so it is divisible by 2.

46200 is a composite number with 96 divisors. Its prime factorisation is $2^{3}$ × 3 × $5^{2}$ × 7 × 11. Divisors (96): 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 20, 21, 22 … 46200.

Number

Pick any whole number from 1 to 100,000.

46200 = 2^{3} \times 3 \times 5^{2} \times 7 \times 11

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How to work it out

1
What is special about 46200: a Harshad number: divisible by its digit sum 12.
2
46200 is composite. Its prime factorisation is
$46200 = 2^{3} \times 3 \times 5^{2} \times 7 \times 11$
3
The divisors add up to 178560; without 46200 itself that is 132360, so 46200 is abundant (132360 is more than 46200). Euler's totient φ(46200) = 9600 numbers up to 46200 share no factor with it.
4
The digits of 46200 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 132 steps to reach 1.

LaTeX source of the formulas on this page

\[ 46200 = 2^{3} \times 3 \times 5^{2} \times 7 \times 11 \]

46200 at a glance

Property	Value
Type	composite
Number of divisors	96
Sum of divisors	178560
Euler totient φ(n)	9600
Square	2134440000
Cube	98611128000000
Square root	214.941853 (= 10√462)
Digit sum / digital root	12 / 3
Collatz steps to 1	132
Scientific notation	4.62 × $10^{4}$

46200 in other forms

Form	Value
In words	forty-six thousand two hundred
Binary (base 2)	1011010001111000
Octal (base 8)	132170
Hexadecimal (base 16)	B478
Base 3	2100101010
As time	46200 seconds = 12 h 50 min 0 s

Is 46200 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (46200 ÷ 2 = 23100)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (46200 ÷ 3 = 15400)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (46200 ÷ 4 = 11550)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (46200 ÷ 5 = 9240)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (46200 ÷ 6 = 7700)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (46200 ÷ 7 = 6600)	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 (46200 ÷ 8 = 5775)	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 (46200 ÷ 10 = 4620)	A number is divisible by 10 if the last digit is 0.
11	Yes (46200 ÷ 11 = 4200)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (46200 ÷ 12 = 3850)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 46200 a prime number?

No. 46200 = $2^{3}$ × 3 × $5^{2}$ × 7 × 11, so it is divisible by 2.

What are the factors of 46200?

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 20, 21, 22, 24, 25, 28, 30, 33, 35, 40, 42, 44, 50, 55, 56, 60, 66, 70, 75, 77, 84, 88, 100, 105, 110, 120, 132, 140, 150, 154, 165, 168, 175, 200, 210, 220, 231, 264, 275, 280, 300, 308, 330, 350, 385, 420, 440, 462, 525, 550, 600, 616, 660, 700, 770, 825, 840, 924, 1050, 1100, 1155, 1320, 1400, 1540, 1650, 1848, 1925, 2100, 2200, 2310, 3080, 3300, 3850, 4200, 4620, 5775, 6600, 7700, 9240, 11550, 15400, 23100, 46200.

What is 46200 in binary?

1011010001111000 (hexadecimal B478, octal 132170).

What is the square root of 46200?

About 214.9419, exactly 10√462.

Is 46200 divisible by 3?

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

What is special about the number 46200?

46200 is a Harshad number: divisible by its digit sum 12.