The number 48300

Q: Is 48300 a prime number?

No. 48300 = 2^2 × 3 × 5^2 × 7 × 23, so it is divisible by 2.

48300 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × 3 × $5^{2}$ × 7 × 23. Divisors (72): 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 23, 25, 28 … 48300.

Number

Pick any whole number from 1 to 100,000.

48300 = 2^{2} \times 3 \times 5^{2} \times 7 \times 23

Explain it step by step in chat Make a short video of it

How to work it out

1
What is special about 48300: a Harshad number: divisible by its digit sum 15.
2
48300 is composite. Its prime factorisation is
$48300 = 2^{2} \times 3 \times 5^{2} \times 7 \times 23$
3
The divisors add up to 166656; without 48300 itself that is 118356, so 48300 is abundant (118356 is more than 48300). Euler's totient φ(48300) = 10560 numbers up to 48300 share no factor with it.
4
The digits of 48300 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 44 steps to reach 1.

LaTeX source of the formulas on this page

\[ 48300 = 2^{2} \times 3 \times 5^{2} \times 7 \times 23 \]

48300 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	166656
Euler totient φ(n)	10560
Square	2332890000
Cube	112678587000000
Square root	219.772610 (= 10√483)
Digit sum / digital root	15 / 6
Collatz steps to 1	44
Scientific notation	4.83 × $10^{4}$

48300 in other forms

Form	Value
In words	forty-eight thousand three hundred
Binary (base 2)	1011110010101100
Octal (base 8)	136254
Hexadecimal (base 16)	BCAC
Base 3	2110020220
As time	48300 seconds = 13 h 25 min 0 s

Is 48300 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (48300 ÷ 2 = 24150)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (48300 ÷ 3 = 16100)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (48300 ÷ 4 = 12075)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (48300 ÷ 5 = 9660)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (48300 ÷ 6 = 8050)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (48300 ÷ 7 = 6900)	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 6)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (48300 ÷ 10 = 4830)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 10)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (48300 ÷ 12 = 4025)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 48300 a prime number?

No. 48300 = $2^{2}$ × 3 × $5^{2}$ × 7 × 23, so it is divisible by 2.

What are the factors of 48300?

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 23, 25, 28, 30, 35, 42, 46, 50, 60, 69, 70, 75, 84, 92, 100, 105, 115, 138, 140, 150, 161, 175, 210, 230, 276, 300, 322, 345, 350, 420, 460, 483, 525, 575, 644, 690, 700, 805, 966, 1050, 1150, 1380, 1610, 1725, 1932, 2100, 2300, 2415, 3220, 3450, 4025, 4830, 6900, 8050, 9660, 12075, 16100, 24150, 48300.

What is 48300 in binary?

1011110010101100 (hexadecimal BCAC, octal 136254).

What is the square root of 48300?

About 219.7726, exactly 10√483.

Is 48300 divisible by 3?

Yes. Its digits add up to 15, a multiple of 3.

What is special about the number 48300?

48300 is a Harshad number: divisible by its digit sum 15.